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Related papers: A dynamical proof of the van der Corput inequality

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We investigate the asymptotic behavior of the solutions to the Klein-Gordon and Dirac equations using the local spatial averaging approach to Bohr's correspondence principle in the large principal quantum number regime. The procedure is…

Quantum Physics · Physics 2022-10-18 K. G. Hernández , S. E. Aguilar , J. Bernal

Similarly to $\beta$-adic van der Corput sequences, abstract van der Corput sequences can be defined for abstract numeration systems. Under some assumptions, these sequences are low discrepancy sequences. The discrepancy function is…

Number Theory · Mathematics 2010-01-23 Wolfgang Steiner

We show how the Gelfand spectrum of certain commutative operator algebras can be studied based on the theorem of Stone and von Neumann. The method presented is a natural addition to the tools of quantum spectral synthesis, which were…

Functional Analysis · Mathematics 2024-10-31 Robert Fulsche , Oliver Fürst

The aim of this paper is twofold. First we prove a theorem of extension of sections of a coherent subquotient of a hermitian vector bundle on a complex analytic space with control of the norms, without any of the smoothness assumptions that…

Number Theory · Mathematics 2007-05-23 Hugues Randriam

We say that a contractive Hilbert space operator is universal if there is a natural surjection from its generated C*-algebra to the C*-algebra generated by any other contraction. A universal contraction may be irreducible or a direct sum of…

Operator Algebras · Mathematics 2019-05-06 Kristin Courtney , David Sherman

In this note, we present a version of Hoeffding's inequality in a continuous-time setting, where the data stream comes from a uniformly ergodic diffusion process. Similar to the well-studied case of Hoeffding's inequality for discrete-time…

Probability · Mathematics 2019-03-26 Michael C. H. Choi , Evelyn Li

C*-algebras are widely used in mathematical physics to represent the observables of physical systems, and are sometimes taken as the starting point for rigorous formulations of quantum mechanics and classical statistical mechanics.…

Functional Analysis · Mathematics 2007-05-23 Miguel Carrion-Alvarez

The inverse conjecture for the Gowers norms $U^d(V)$ for finite-dimensional vector spaces $V$ over a finite field $\F$ asserts, roughly speaking, that a bounded function $f$ has large Gowers norm $\|f\|_{U^d(V)}$ if and only if it…

Combinatorics · Mathematics 2012-01-04 Terence Tao , Tamar Ziegler

Motivated by the study of periods of automorphic forms and relative trace formulae, we develop the theory of descent necessary to study orbital integrals arising in the fundamental lemma for a general class of symmetric spaces over a…

Number Theory · Mathematics 2021-08-17 Spencer Leslie

We give an alternative, simple method to prove isoperimetric inequalities over the hypercube. In particular, we show: 1. An elementary proof of classical isoperimetric inequalities of Talagrand, as well as a stronger isoperimetric result…

Combinatorics · Mathematics 2025-07-22 Ronen Eldan , Guy Kindler , Noam Lifshitz , Dor Minzer

In this paper we study variational inequalities in a real Hilbert space, which are governed by a strongly monotone and Lipschitz continuous operator $F$ over a closed and convex set $C$. We assume that the set $C$ can be outerly…

Optimization and Control · Mathematics 2017-02-06 Aviv Gibali , Simeon Reich , Rafal Zalas

We prove a generalization of van der Corput's Difference Theorem in the theory of uniform distribution by establishing a connection with unitary operators that have Lebesgue spectrum. This allows us to show, for example, that if $(x_n)_{n =…

Dynamical Systems · Mathematics 2024-08-16 Sohail Farhangi

We construct a general class of correspondences on hyperelliptic Riemann surfaces of arbitrary genus that combine finitely many Fuchsian genus zero orbifold groups and Blaschke products. As an intermediate step, we first construct analytic…

Dynamical Systems · Mathematics 2025-08-27 Sabyasachi Mukherjee , S. Viswanathan

We provide new complexity information for the convergence of the Hybrid Steepest Descent Method for solving the Variational Inequality Problem for a strict contraction on Hilbert space over a closed convex set C given either as the fixed…

Logic · Mathematics 2016-10-04 Daniel Körnlein

Learning from non-independent and non-identically distributed data poses a persistent challenge in statistical learning. In this study, we introduce data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert…

Machine Learning · Computer Science 2025-07-11 Erfan Mirzaei , Andreas Maurer , Vladimir R. Kostic , Massimiliano Pontil

Human similarity judgments are inconsistent with Euclidean, Hamming, Mahalanobis, and the majority of measures used in the extensive literatures on similarity and dissimilarity. From intrinsic properties of brain circuitry, we derive…

Neurons and Cognition · Quantitative Biology 2017-09-27 Antonio M Rodriguez , Richard Granger

In this paper we prove the strong and time-averaged strong convergence to equilibrium for solutions (with general initial data) of the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. The assumption on the collision…

Analysis of PDEs · Mathematics 2023-03-07 Bocheng Liu , Xuguang Lu

We study persistence probabilities of Hermite processes. As a tool, we derive a general decorrelation inequality for the Rosenblatt process, which is reminiscent of Slepian's lemma for Gaussian processes or the FKG inequality and which may…

Probability · Mathematics 2016-07-19 Frank Aurzada , Christian Mönch

The radius of comparison is an invariant for unital C*-algebras which extends the theory of covering dimension to noncommutative spaces. We extend its definition to general C*-algebras, and give an algebraic (as opposed to…

Operator Algebras · Mathematics 2010-08-25 Bruce Blackadar , Leonel Robert , Aaron P. Tikuisis , Andrew S. Toms , Wilhelm Winter

In this partly expository paper we study van der Corput sets in $\Z^d$, with a focus on connections with harmonic analysis and recurrence properties of measure preserving dynamical systems. We prove multidimensional versions of some…

Dynamical Systems · Mathematics 2007-10-26 Vitaly Bergelson , Emmanuel Lesigne