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  • On the hyperbolic distance of n -times punctured spheres
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Toshiyuki Sugawa, Matti Vuorinen, Tanran Zhang

    The shortest closed geodesic in a hyperbolic surface X is called a systole of X. When X is an n-times punctured sphere \(\mathbb{C}\widehat\backslash A\) where \(A \subset \widehat {\mathbb{C}}\) is a finite set of cardinality n ≥ 4, we define a quantity Q(A) in terms of cross ratios of quadruples in A so that Q(A) is quantitatively comparable with the systole length of X. We next propose a method

    更新日期:2020-08-10
  • Central limit theorems for group actions which are exponentially mixing of all orders
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Michael Björklund, Alexander Gorodnik

    In this paper we establish a general dynamical Central Limit Theorem (CLT) for group actions which are exponentially mixing of all orders. In particular, the main result applies to Cartan flows on finite-volume quotients of simple Lie groups. Our proof uses a novel relativization of the classical method of cumulants, which should be of independent interest. As a sample application of our techniques

    更新日期:2020-08-08
  • Improved estimates for polynomial Roth type theorems in finite fields
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Dong Dong, Xiaochun Li, Will Sawin

    We prove that, under certain conditions on the function pair ϕ1 and ϕ2, the bilinear average \({q^{- 1}}\sum\nolimits_{y \in {\mathbb{F}_q}} {{f_1}\left({x + {\varphi _2}\left(y \right)} \right){f_2}\left({x + {\varphi _2}\left(y \right)} \right)} \) along the curve (ϕ1, ϕ2) satisfies a certain decay estimate. As a consequence, Roth type theorems hold in the setting of finite fields. In particular

    更新日期:2020-08-08
  • Blow-up profiles and life beyond blow-up in the fully parabolic Keller-Segel system
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Michael Winkler

    The fully parabolic Keller-Segel system is considered in n-dimensional balls with n ≥ 2. Pointwise time-independent estimates are derived for arbitrary radially symmetric solutions. These are firstly used to assert that any radial classical solution which blows up in finite time possesses a uniquely determined blow-up profile which satisfies an associated pointwise upper inequality. Secondly, in conjunction

    更新日期:2020-08-08
  • Feynman path integrals for magnetic Schrödinger operators on infinite weighted graphs
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Batu Güneysu, Matthias Keller

    We prove a Feynman path integral formula for the unitary group exp(—itLυ,θ), t ≥ 0, associated with a discrete magnetic Schrödinger operator Lυ,θ on a large class of weighted infinite graphs. As a consequence, we get a new Kato-Simon estimate \(\left| {\exp \left({- it{L_{v,\theta}}} \right)\left({x,y} \right)} \right| \le \exp \left({- t{L_{- \deg ,0}}} \right)\left({x,y} \right),\) which controls

    更新日期:2020-08-08
  • Strongly automorphic mappings and Julia sets of uniformly quasiregular mappings
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Alastair Fletcher, Douglas Macclure

    A theorem of Ritt states the Poincaré linearizer L of a rational map f at a repelling fixed point is periodic only if f is conjugate to a power of z, a Chebyshev polynomial or a Lattes map. The converse, except for the case where the fixed pointis an endpoint of the interval Julia set for a Chebyshev polynomial, is also true. In this paper, we prove the analogous statement in the setting of strongly

    更新日期:2020-08-08
  • Planck-scale distribution of nodal length of arithmetic random waves
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Jacques Benatar, Domenico Marinucci, Igor Wigman

    We study the nodal length of random toral Laplace eigenfunctions (“arithmetic random waves”) restricted to decreasing domains (“shrinking balls”), all the way down to Planck scale. We find that, up to a natural scaling, for “generic” energies the variance of the restricted nodal length obeys the same asymptotic law as the total nodal length, and these are asymptotically fully correlated. This, among

    更新日期:2020-08-08
  • Extreme points in the isometric embedding problem for model spaces
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Leonid Golinskii

    In 1996 A. Aleksandrov solved the isometric embedding problem for the model spaces KΘ with an arbitrary inner function Θ.We find all extreme points of this convex set of measures in the case when & is a finite Blaschke product, and obtain some partial results for generic inner functions.

    更新日期:2020-08-08
  • Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Wencai Liu, Darren C. Ong

    In this paper, we consider the Schrödinger equation, \(Hu = - {u^"} + \left({V\left(x \right) + {V_0}\left(x \right)} \right)u = Eu,\) where V0(x) is 1-periodic and V(x) is a decaying perturbation. By Floquet theory, the spectrum of H0 = − ∇2 + V0 is purely absolutely continuous and consists of a union of closed intervals (often referred to as spectral bands). Given any finite set of points \(\left\{{{E_j}}

    更新日期:2020-08-08
  • A smooth zero-entropy diffeomorphism whose product with itself is loosely Bernoulli
    J. Anal. Math. (IF 0.949) Pub Date : 2020-08-08
    Marlies Gerber, Philipp Kunde

    Let M be a smooth compact connected manifold of dimension d ≥ 2, possibly with boundary, that admits a smooth effective \({\mathbb{T}^2}\)-action \({\cal S} = {\left\{{{S_{\alpha ,\beta}}} \right\}_{\left({\alpha ,\beta} \right) \in {\mathbb{T}^2}}}\) preserving a smooth volume v, and let \({\cal B}\) be the C∞ closure of \(\left\{{h\, \circ {S_{\alpha ,\beta}} \circ {h^{- 1}}:h \in {\rm{Dif}}{{\r

    更新日期:2020-08-08
  • Sharp regularity for the inhomogeneous porous medium equation
    J. Anal. Math. (IF 0.949) Pub Date : 2020-03-25
    Damião J. Araújo, Anderson F. Maia, José Miguel Urbano

    We show that locally bounded solutions of the inhomogeneous porous medium equation $$u_{t}-\operatorname{div}\left(m|u|^{m-1} \nabla u\right)=f \in L^{q, r}, \quad m>1$$ are locally Hölder continuous, with exponent $$\gamma = \min \{ {{\alpha _0^ - } \over m},\;{{[(2q - n)r - 2q]} \over {q[(mr - (m - 1)]}}\} ,$$ where α0 denotes the optimal Hölder exponent for solutions of the homogeneous case. The

    更新日期:2020-03-25
  • Cesàro bounded operators in Banach spaces
    J. Anal. Math. (IF 0.949) Pub Date : 2020-03-25
    Teresa Bermúdez, Antonio Bonilla, Vladimír Müller, Alfredo Peris

    We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Cesàro bounded and strongly Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing (hence, not power bounded) absolutely Cesàro bounded operators on ℓp(ℕ), 1 ≤ p < ∞, and provide examples of uniformly

    更新日期:2020-03-25
  • A Schwarz lemma at the boundary on complex Hilbert balls and applications to starlike mappings
    J. Anal. Math. (IF 0.949) Pub Date : 2020-03-23
    Ian Graham, Hidetaka Hamada, Gabriela Kohr

    In this paper, we prove a Schwarz lemma at the boundary for holomorphic mappings f between Hilbert balls, and obtain related consequences. Especially, we obtain estimations of ∥Df(z0)∥ on the holomorphic tangent space for holomorphic mappings f or for homogeneous polynomial mappings f between Hilbert balls. Next, we prove the boundary rigidity theorem for holomorphic self-mappings of a Hilbert ball

    更新日期:2020-03-23
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