• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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 • 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
• 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
• 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
• 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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