• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
James Williams

In this note we show that if p is an odd prime and G is a powerful p-group with N ≤ Gp and N normal in G, then N is powerfully nilpotent. An analogous result is proved for p = 2 when N ≤ G4.

更新日期：2020-09-23
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
George Glauberman, Robert Guralnick, Justin Lynd, Gabriel Navarro

Suppose that p is an odd prime and G is a finite group having no normal non-trivial p′-subgroup. We show that if a is an automorphism of G of p-power order centralizing a Sylow p-group of G, then a is inner.

更新日期：2020-09-23
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
Andrea Pinamonti, Gareth Speight

We show that any Carnot group $$\mathbb{G}$$ with sufficiently many deformable directions contains a measure zero set N such that every Lipschitz map $$f:\mathbb{G}\rightarrow \mathbb{R}$$ is differentiable at some point of N. We also prove that model filiform groups satisfy this condition, extending some previous results to a class of Carnot groups of arbitrarily high step. Essential to our work is

更新日期：2020-09-23
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
Nathan Keller, Ohad Klein

The Fourier-Walsh expansion of a Boolean function f: {0, 1}n → {0, 1} is its unique representation as a multilinear polynomial. The Kindler-Safra theorem (2002) asserts that if in the expansion of f, the total weight on coefficients beyond degree k is very small, then f can be approximated by a Boolean-valued function depending on at most O(2k) variables. In this paper we prove a similar theorem for

更新日期：2020-09-23
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
Ming Jin, Guangbin Ren, Irene Sabadini

The slice Dirac operator over octonions is a slice counterpart of the Dirac operator over quaternions. It involves a new theory of stem functions, which is the extension from the commutative O(1) case to the non-commutative O(3) case. For functions in the kernel of the slice Dirac operator over octonions, we establish the representation formula, the Cauchy integral formula (and, more in general, the

更新日期：2020-09-23
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
Elias Katsoulis

We establish the Hao–Ng isomorphism for generalized gauge actions of locally compact abelian groups on product systems over abelian lattice orders and we then use it to explore Takai duality in this context. As an application we generalize some recent work of Schafhauser.

更新日期：2020-09-23
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
Willian Hans Goes Corrêa

We study the complex interpolation and derivation process induced by a family of Orlicz sequence spaces. We present a concrete example of an interpolation family of three spaces inducing a centralizer that cannot be obtained from complex interpolation of two spaces.

更新日期：2020-09-23
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
Moritz Firsching

We describe an algorithm to enumerate polytopes. This algorithm is then implemented to give a complete classification of combinatorial spheres of dimension 3 with 9 vertices and decide polytopality of those spheres. In order to decide polytopality, we generate polytopes by adding suitable points to polytopes with less than 9 vertices and therefore realize as many as possible of the combinatorial spheres

更新日期：2020-09-23
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
Nicholas Ramsey

We consider cardinal invariants related to Shelah’s model-theoretic tree properties and the relations that obtain between them. From strong colorings, we construct theories T with κcdt(T) > κsct(T) + κinp(T). We show that these invariants have distinct structural consequences, by investigating their effect on the decay of saturation in ultrapowers. This answers some questions of Shelah.

更新日期：2020-09-23
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
Fernando Albiac, José L. Ansorena, Marek Cúth, Michal Doucha

This paper initiates the study of the structure of a new class of p-Banach spaces, 0

更新日期：2020-09-23
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
Zakhar Kabluchko, Joscha Prochno, Christoph Thäle

We study the volume of the intersection of two unit balls from one of the classical matrix ensembles GOE, GUE and GSE, as the dimension tends to infinity. This can be regarded as a matrix analogue of a result of Schechtman and Schmuckenschläger for classical ℓp-balls [Schechtman and Schmuckenschläger, GAFA Lecture Notes, 1991]. The proof of our result is based on two ingredients, which are of independent

更新日期：2020-09-02
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
Van Cyr, Bryna Kra

A subshift with linear block complexity has at most countably many ergodic measures, and we continue the study of the relation between such complexity and the invariant measures. By constructing minimal subshifts whose block complexity is arbitrarily close to linear but have uncountably many ergodic measures, we show that this behavior fails as soon as the block complexity is superlinear. With a different

更新日期：2020-09-02
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
Pantelis E. Eleftheriou, Ayhan Günaydin, Philipp Hieronymi

We study sets and groups definable in tame expansions of o-minimal structures. Let $$\widetilde{\cal M} = \left\langle {{\cal M},P} \right\rangle$$ be an expansion of an o-minimal $${\cal L}$$-structure $${\cal M}$$ by a dense set P. We impose three tameness conditions on $$\widetilde{\cal M}$$ and prove a structure theorem for definable sets and functions in analogy with the cell decomposition theorem

更新日期：2020-09-02
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
Niclas Technau, Martin Widmer

We prove a counting theorem concerning the number of lattice points for the dual lattices of weakly admissible lattices in an inhomogeneously expanding box. The error term is expressed in terms of a certain function ν(Γ⊥, ·) of the dual lattice Γ⊥, and we carefully analyse the relation of this quantity with ν(Γ, ·). In particular, we show that ν(Γ⊥, ·) = ν(Γ, ·) for any unimodular lattice of rank 2

更新日期：2020-09-02
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
Matteo Costantini

We consider Lyapunov exponents for flat bundles over hyperbolic curves defined via parallel transport over the geodesic flow. We refine a lower bound obtained by Eskin, Kontsevich, Möller and Zorich showing that the sum of the first k exponents is greater than or equal to the sum of the degree of any rank k holomorphic subbundle of the flat bundle and the asymptotic degree of its equivariant developing

更新日期：2020-09-02
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
Roberto Alvarenga

The graph of a Hecke operator encodes all information about the action of this operator on automorphic forms over a global function field. These graphs were introduced by Lorscheid in [16] for PGL2 and generalized to GLn in [1]. After reviewing some general properties, we explain the connection to the Hall algebra of the function field. In the case of an elliptic function field, we can use structure

更新日期：2020-09-02
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
Saharon Shelah

We would like to build Abelian groups (or R-modules) which on the one hand are quite free, say ℵω+1-free, and on the other hand are complicated in a suitable sense. We choose as our test problem one having no nontrivial homomorphism to ℤ (known classically for ℵ1-free, recently for ℵn-free). We succeed to prove the existence of even $${\aleph _{{\omega _1} \cdot n}}$$-free ones. This requires building

更新日期：2020-09-02
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
Balázs Bárány, Antti Käenmäki, Ian D. Morris

In topics such as the thermodynamic formalism of linear cocycles, the dimension theory of self-affine sets, and the theory of random matrix products, it has often been found useful to assume positivity of the matrix entries in order to simplify or make feasible certain types of calculation. It is natural to ask how positivity may be relaxed or generalised in a way which enables similar calculations

更新日期：2020-09-02
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
Mihir Sheth

The Lubin-Tate moduli space $$X_0^{{\rm{rig}}}$$ is a p-adic analytic open unit polydisc which parametrizes deformations of a formal group H0 of finite height defined over an algebraically closed field of characteristic p. It is known that the natural action of the automorphism group Aut(H0)on $$X_0^{{\rm{rig}}}$$ gives rise to locally analytic representations on the topological duals of the spaces

更新日期：2020-09-02
• Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
Paul F. X. Müller, Markus Passenbrunner

We prove the analogue of the Martingale Convergence Theorem for polynomial spline sequences. Given a natural number k and a sequence (ti) of knots in [0, 1] with multiplicity ≤ k − 1, we let Pn be the orthogonal projection onto the space of spline polynomials in [0, 1] of degree k − 1 corresponding to the grid $$\left( {{t_i}} \right)_{i = 1}^n$$. Let X be a Banach space with the Radon—Nikodým property

更新日期：2020-09-02
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
Vyacheslav Futorny, Dimitar Grantcharov, Luis Enrique Ramirez, Pablo Zadunaisky

In the present paper we study Gelfand-Tsetlin modules defined in terms of BGG differential operators. The structure of these modules is described with the aid of the Postnikov-Stanley polynomials introduced in [PS09]. These polynomials are used to identify the action of the Gelfand-Tsetlin subalgebra on the BGG operators. We also provide explicit bases of the corresponding Gelfand-Tsetlin modules and

更新日期：2020-07-27
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
Arie Levit

A sequence of orbifolds corresponding to pairwise non-conjugate congruence lattices in a higher rank semisimple group over zero characteristic local fields is Benjamini-Schramm convergent to the universal cover.

更新日期：2020-07-27
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
Timothy C. Burness, Scott Harper

Let G be a finite 2-generated non-cyclic group. The spread of G is the largest integer k such that for any nontrivial elements x1, …, xk, there exists y ∈ G such that G = 〈xi, y〉 for all i. The more restrictive notion of uniform spread, denoted u(G), requires y to be chosen from a fixed conjugacy class of G, and a theorem of Breuer, Guralnick and Kantor states that u(G) ⩾ 2 for every non-abelian finite

更新日期：2020-07-27
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
Klaudiusz Czudek, Tomasz Szarek

The central limit theorem for Markov chains generated by iterated function systems consisting of orientation-preserving homeomorphisms of the interval is proved. We study also ergodicity of such systems.

更新日期：2020-07-27
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
Miguel Berasategui, Daniel Carando

We show that, for 1 < p ≤ 2, the space Lp(ℝd) does not admit unconditional Schauder frames {fi, f′i}i∈ℕ where {fi} is a sequence of translates of finitely many functions and {f′i} is seminormalized. In fact, the only subspaces of Lp(ℝd) admitting such Banach frames are those isomorphic to ℓp. On the other hand, if 2 < p < +∞ and {λi}i∈ℕ ⊆ ℝd is an unbounded sequence, there is a subsequence {λi}i∈ℕ

更新日期：2020-07-27
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
Lingling Huang, Jun Wu, Jian Xu

In the one-dimensional Diophantine approximation, by using the continued fractions, Khintchine’s theorem and Jarnik’s theorem are concerned with the growth of the large partial quotients, while the improvability of Dirichlet’s theorem is concerned with the growth of the product of consecutive partial quotients. This paper aims to establish a complete characterization on the metric properties of the

更新日期：2020-07-27
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
Hongming Nie, Kevin M. Pilgrim

We investigate boundedness of hyperbolic components in the moduli space of Newton maps. For quartic maps, (i) we prove hyperbolic components possessing two distinct attracting cycles each of period at least two are bounded, and (ii) we characterize the possible points on the boundary at infinity for some other types of hyperbolic components. For general maps, we prove hyperbolic components whose elements

更新日期：2020-07-27
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
Yong Jiao, Fedor Sukochev, Dmitriy Zanin

This paper deals with new phenomena appearing in the structure of Banach spaces arising in noncommutative integration theory. Let E be a fully symmetric Banach function space on [0, 1] and M be a finite von Neumann algebra. Let [xk] be the closed subspace spanned by a sequence (xk) of freely independent mean zero random variables from E(ℳ). The subspace [xk] is complemented in E(ℳ) if and only if the

更新日期：2020-07-27
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
Jacob Fox, János Pach, Andrew Suk

We consider m-colorings of the edges of a complete graph, where each color class is defined semi-algebraically with bounded complexity. The case m = 2 was first studied by Alon et al., who applied this framework to obtain surprisingly strong Ramsey-type results for intersection graphs of geometric objects and for other graphs arising in computational geometry. Considering larger values of m is relevant

更新日期：2020-07-27
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
Miyu Suzuki

Let E/F be a quadratic extension of non-Archimedean local fields of characteristic 0. Let D be the unique quaternion division algebra over F and fix an embedding of E to D. Then, GLm(D) can be regarded as a subgroup of GL2m(E). Using the method of Matringe, we classify irreducible generic GLm(D)-distinguished representations of GL2m(E) in terms of Zelevinsky classification. Rewriting the classification

更新日期：2020-07-27
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Marius Tărnăuceanu

In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Weikun He

We study random walks on GLd(ℝ) whose proximal dimension r is larger than 1 and whose limit set in the Grassmannian Grr,d(ℝ) is not contained any Schubert variety. These random walks, without being proximal, behave in many ways like proximal ones. Among other results, we establish a Hölder-type regularity for the stationary measure on the Grassmannian associated to these random walks. Using this and

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Jun Seok Oh, Qinghai Zhong

Let G be a finite group and exp(G) = lcm{ord(g) ∣ g ∈ G}. A finite unordered sequence of terms from G, where repetition is allowed, is a product-one sequence if its terms can be ordered such that their product equals the identity element of G. We denote by s(G)(or E(G) respectively) the smallest integer ℓ such that every sequence of length at least ℓ has a product-one subsequence of length exp(G)(or

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Nikolay Moshchevitin, Brendan Murphy, Ilya Shkredov

We prove bounds for the popularity of products of sets with weak additive structure, and use these bounds to prove results about continued fractions. Namely, considering Zaremba’s set modulo p, that is the set of all a such that $${a \over p} = [{a_1}, \ldots ,{a_s}]$$ has bounded partial quotients, aj ⩽ M, we obtain a sharp upper bound for the cardinality of this set.

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Maria Chudnovsky, Alex Scott, Paul Seymour, Sophie Spirkl

Let G be a graph, and let fG be the sum of (−1)∣A∣, over all stable sets A. If G is a cycle with length divisible by three, then fG = ±2. Motivated by topological considerations, G. Kalai and R. Meshulam [8] made the conjecture that, if no induced cycle of a graph G has length divisible by three, then ∣fG∣ ≤ 1. We prove this conjecture.

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Filippo Callegaro, Mario Salvetti

We consider the universal family Edn of superelliptic curves: each curve Σdn in the family is a d-fold covering of the unit disk, totally ramified over aset P of n distinct points; $$\Sigma _n^d \hookrightarrow E_n^d \to {{\rm{C}}_n}$$ is a fiber bundle, where Cn is the configuration space of n distinct points. We find that Edn is the classifying space for the complex braid group of type B(d, d, n)

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Jun Wang, Xiao Yao

Let f be a meromorphic function in the complex plane. A value θ ∈ [0, 2π) is called a Julia limiting direction of f if there is an unbounded sequence {zn} in the Julia set J(f) satisfying limn→∞ arg zn = θ (mod 2π). We denote by L(f) the set of all Julia limiting directions of f. Our main result is that, for any non-empty compact set E ⊆ [0, 2π) and ρ ∈ [0, ∞], there are an entire function f of infinite

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Sheldy Ombrosi, Carlos Pérez, Ezequiel Rela, Israel P. Rivera-Ríos

In this note we generalize the definition of the Fujii-Wilson condition providing quantitative characterizations of some interesting classes of weights, such as A∞, Aweak∞ and Cp, in terms of BMO type spaces suited to them. We will provide as well some self improvement properties for some of those generalized BMO spaces and some quantitative estimates for Bloom’s BMO type spaces.

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Matija Bucić, Matthew Kwan, Alexey Pokrovskiy, Benny Sudakov, Tuan Tran, Adam Zsolt Wagner

How long a monotone path can one always find in any edge-ordering of the complete graph Kn? This appealing question was first asked by Chvátal and Komlós in 1971, and has since attracted the attention of many researchers, inspiring a variety of related problems. The prevailing conjecture is that one can always find a monotone path of linear length, but until now the best known lower bound was n2/3-o(1)

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Danijela Damjanović, Disheng Xu

We prove global smooth classification results for Anosov ℤk actions on general compact manifolds, under certain irreduciblity conditions and the presence of sufficiently many Anosov elements. In particular, we remove all the uniform control assumptions which were used in all the previous results towards the Katok-Spatzier global rigidity conjecture on general manifolds. The main idea is to create a

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
William Woods

Let p > 2 be a prime, k a finite field of characteristic p, and G a nilpotent-by-finite compact p-adic analytic group. Write kG for the completed group ring of G over k. We show that kG is a catenary ring.

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Sergei V. Kislyakov, Ilya K. Zlotnikov

Let (X, μ) be a space with a finite measure μ, let A and B be w*-closed subalgebras of L∞(μ), and let C and D be closed subspaces of Lp(μ) (1 < p < ∞) that are modules over A and B, respectively. Under certain additional assumptions, the couple (C ∩ D, C ∩ D ∩ L∞>(μ)) is K-closed in (Lp(μ), L∞(μ)). This statement covers, in particular, two cases analyzed previously: that of Hardy spaces on the two-dimensional

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Antonio Giambruno, Daniela La Mattina

In this paper we prove that if A is any algebra with involution * satisfying a non-trivial polynomial identity, then its sequence of *-codimensions is eventually non-decreasing. Furthermore, by making use of the *-exponent we reconstruct the only two *-algebras, up to T*-equivalence, generating varieties of almost polynomial growth. As a third result we characterize the varieties of algebras with involution

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Carl Bürger, Max Pitz

In 1978, Richard Rado showed that every edge-coloured complete graph of countably infinite order can be partitioned into monochromatic paths of different colours. He asked whether this remains true for uncountable complete graphs and a notion of generalised paths. In 2016, Daniel Soukup answered this in the affirmative and conjectured that a similar result should hold for complete bipartite graphs

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Junehyuk Jung

We prove Polterovich’s conjecture concerning the growth of the number of nodal domains for eigenfunctions on a unit square domain, under the assumption that the eigenfunctions do not have any singular points.

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Boris Bukh, Christopher Cox

How can d+k vectors in ℝd be arranged so that they are as close to orthogonal as possible? In particular, define θ(d, k) := minX maxx≠y∈X |〈x, y〉 | where the minimum is taken over all collections of d + k unit vectors X ⊆ ℝd. In this paper, we focus on the case here k is fixed and d → ∞. In establishing bounds on θ(d, k), we find an intimate connection to the existence of systems of $$\left(\begin{array}{c}k+1\\ 更新日期：2020-06-05 • Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05 Barbara Anna Balázs, Szabolcs Mészáros We prove an Amitsur–Levitzki-type theorem for Grassmann algebras, stating that the minimal degree of a standard identity that is a polynomial identity of the ring of n × n matrices over the m-generated Grassmann algebra is at least \(2\lfloor\frac{m}{2}\rfloor+4n-4$$ for all n, m ≥ 2 and this bound is sharp for m = 2,3 and any n ≥ 2. The arguments are purely combinatorial, based on computing sums of

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Juan Bès, Dimitris Papathanasiou

We show that several convolution operators on the space of entire functions, such as the MacLane operator, support a dense hypercyclic algebra that is not finitely generated. Birkhoff’s operator also has this property on the space of complex-valued smooth functions on the real line.

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Andrey Gogolev, Boris Kalinin, Victoria Sadovskaya

We study the regularity of the conjugacy between an Anosov automorphism L of a torus and its small perturbation. We assume that L has no more than two eigenvalues of the same modulus and that L4 is irreducible over ℚ. We consider a volume-preserving C1-small perturbation f of L. We show that if Lyapunov exponents of f with respect to the volume are the same as Lyapunov exponents of L, then f is C1+Hölder

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Urtzi Buijs, Yves Félix, Aniceto Murillo, Daniel Tanré

Extending the model of the interval, we explicitly define for each n ≥ 0 a free complete differential graded Lie algebra $$\mathfrak{L}_n$$ generated by the simplices of Δn, with desuspended degrees, in which the vertices are Maurer-Cartan elements and the differential extends the simplicial chain complex of the standard n-simplex. The family $$\{\mathfrak{L{_\bullet}}\}_{n\geq0}$$ is endowed with

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Richard Lechner, Pavlos Motakis, Paul F. X. Müller, Thomas Schlumprecht

We introduce the concept of strategically reproducible bases in Banach spaces and show that operators which have large diagonal with respect to strategically reproducible bases are factors of the identity. We give several examples of classical Banach spaces in which the Haar system is strategically reproducible: multi-parameter Lebesgue spaces, mixed-norm Hardy spaces and most significantly the space

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Leo Margolis, Ofir Schnabel

Similarly to how the classical group ring isomorphism problem asks, for a commutative ring R, which information about a finite group G is encoded in the group ring RG, the twisted group ring isomorphism problem asks which information about G is encoded in all the twisted group rings of G over R. We investigate this problem over fields. We start with abelian groups and show how the results depend on

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Soumitra Ghara

Let Möb denote the group of biholomorphic automorphisms of the unit disc and (Möb · T) be the orbit of a Hilbert space operator T under the action of Möb. If the quotient , where is the similarity between two operators is a singleton, then the operator T is said to be weakly homogeneous. In this paper, we obtain a criterion to determine if the operator Mz of multiplication by the coordinate function

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Eliana Barriga

We study definably compact definably connected groups definable in a sufficiently saturated real closed field R. Our main result is that for such a kind of groups G that are also abelian, there is a Zariski-connected R-algebraic group H such that the o-minimal universal covering group of G is, up to a locally definable isomorphism, an open connected locally definable subgroup $$\mathcal{W}$$ of the

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Hidefumi Ohsugi, Akiyoshi Tsuchiya

Stanley introduced a lattice polytope $$\mathscr{C}_P$$ arising from a finite poset P, which is called the chain polytope of P. The geometric structure of $$\mathscr{C}_P$$ has good relations with the combinatorial structure of P. In particular, the Ehrhart polynomial of $$\mathscr{C}_P$$ is given by the order polynomial of P. In the present paper, associated to P, we introduce a lattice polytope ℰP

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Michael Lieberman, Jiří Rosický, Sebastien Vasey

Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from [LRV19b], we examine set-theoretic problems related to internal sizes and prove several Löwenheim–Skolem theorems for accessible categories. For example, assuming the singular cardinal hypothesis, we show that a large accessible category has an object in all

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Hezi Halawi, Avner Segal

In this paper, we study the reducibility of degenerate principal series of the simple, simply-connected exceptional group of type E6. Furthermore, we calculate the maximal semi-simple subrepresentation and quotient of these representations.

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Konrad Engel, Themis Mitsis, Christos Pelekis, Christian Reiher

Let n be an integer with n ≥ 2. A set A ⊆ ℝn is called an antichain (resp. weak antichain) if it does not contain two distinct elements x = (x1, …, xn) and y = (y1, …, yn) satisfying xi ≤ yi (resp. xi < yi) for all i ∈ {1, …, n}. We show that the Hausdorff dimension of a weak antichain A in the n-dimensional unit cube [0, 1]n is at most n − 1 and that the (n − 1)-dimensional Hausdorff measure of A

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Andreas Maurischat

This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for reduced algebraic group schemes over any iterative differential field which is finitely generated over its algebraically closed field of constants. We also introduce the notion of equivalence of iterative derivations on a

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Moti Gitik

We deal with some questions related to κ-compact cardinals.

更新日期：2020-05-20
Contents have been reproduced by permission of the publishers.

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