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The aim of this paper is to establish a few qualitative uncertainty principles for the windowed Opdam-Cherednik transform on weighted modulation spaces associated with this transform. In particular, we obtain the Cowling-Price's, Hardy's…

Functional Analysis · Mathematics 2022-10-17 Shyam Swarup Mondal , Anirudha Poria

We obtain Fourier inequalities in the weighted $L_p$ spaces for any $1<p<\infty$ involving the Hardy-Ces\`aro and Hardy-Bellman operators. We extend these results to product Hardy spaces for $p\le 1$. Moreover, boundedness of the…

Classical Analysis and ODEs · Mathematics 2022-05-06 Mikhail Dyachenko , Erlan Nursultanov , Sergey Tikhonov , Ferenc Weisz

We review the Cauchy problem for f(R) theories of gravity, in metric and metric-affine for- mulations, pointing out analogies and differences with respect to General Relativity. The role of conformal transformations, effective scalar fields…

General Relativity and Quantum Cosmology · Physics 2011-03-14 S. Capozziello , S. Vignolo

In this paper, we extend the coupled fractional Fourier transform of a complex valued functions to that of the quaternion valued functions on $\mathbb{R}^4$ and call it the quaternion coupled fractional Fourier transform (QCFrFT). We obtain…

General Mathematics · Mathematics 2023-10-02 Bivek Gupta , Amit K. Verma , Ravi P. Agarwal

Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of…

Classical Analysis and ODEs · Mathematics 2011-01-11 H. De Bie , N. De Schepper , F. Sommen

By a systematic development of fundamental concepts of conformable calculus we establish conformable divergence theorem and Green's identities which we combine with some new anisotropic Picone type identities to derive a generalized…

Analysis of PDEs · Mathematics 2024-12-03 Abimbola Abolarinwa , Yisa O Anthony

We obtain a new version of the Uncertainty Principle for functions with Fourier transforms supported on a lacunary set of intervals. This is a generalization of Zygmund's theorem on lacunary trigonometric series to the real line in the…

Classical Analysis and ODEs · Mathematics 2007-05-23 O. Kovrizhkin

In this paper we prove some uncertainty bounds for commutators and anti-commutators of observables in a $C^*$-algebra. We give a short, elementary proof of Robertson's Standard Uncertaity Principle in this setting. We also prove some other…

Operator Algebras · Mathematics 2025-03-25 Saptak Bhattacharya

We consider Schr\"{o}dinger equations with real quadratic Hamiltonians, for which the Wigner distribution of the solution at a given time equals, up to a linear coordinate transformation, the Wigner distribution of the initial condition.…

Analysis of PDEs · Mathematics 2022-11-04 Helge Knutsen

Let $G$ be a locally compact abelian group, and let $\widehat{G}$ denote its dual group, equipped with a Haar measure. A variant of the uncertainty principle states that for any $S \subset G$ and $\Sigma \subset \widehat{G}$, there exists a…

Classical Analysis and ODEs · Mathematics 2025-03-05 Philippe Jaming , Alexander Iosevich , Azita Mayeli

This paper studies the uncertainty principle for spherical $h$-harmonic expansions on the unit sphere of $\mathbb{R}^d$ associated with a weight function invariant under a general finite reflection group, which is in full analogy with the…

Classical Analysis and ODEs · Mathematics 2015-11-18 Han Feng

We extend Hardy's uncertainty principle for a square integrable function and its Fourier transform to the multidimensional case using a symplectic diagonalization. We use this extension to show that Hardy's uncertainty principle is…

Mathematical Physics · Physics 2008-03-07 Maurice de Gosson , Franz Luef

This paper originates from a naive attempt to establish various non-commutative Fourier theoretic inequalities for an inclusion of simple C*-algebras equipped with a conditional expectation of index-finite type. In this setting, we discuss…

Operator Algebras · Mathematics 2026-01-19 Keshab Chandra Bakshi , Satyajit Guin , Sruthymurali

By imposing on the most general renormalizable quantum field theory the requirement of the absence of ultraviolet-divergent renormalizations of the physical parameters (masses and coupling constants) of the theory, finite quantum field…

High Energy Physics - Theory · Physics 2007-05-23 Wolfgang Lucha , Michael Moser

We construct $\delta$-regular sets with $\delta\ge \frac12$ for which the analog of the Bourgain--Dyatlov Fractal Uncertainty Principle fails for the Walsh--Fourier transform.

Classical Analysis and ODEs · Mathematics 2020-09-01 Ciprian Demeter

We consider a uniqueness problem concerning the Fourier coefficients of normalized Cauchy transforms. These problems inherently involve proving a simultaneous approximation phenomenon and establishing the existence of cyclic inner functions…

Complex Variables · Mathematics 2024-10-28 Adem Limani

In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an…

Classical Analysis and ODEs · Mathematics 2007-05-23 Philippe Jaming

The aim of this paper is to prove new uncertainty principles for an integral operator $\tt$ with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of Faris's local uncertainty principle…

Classical Analysis and ODEs · Mathematics 2018-08-27 Saifallah Ghobber , Philippe Jaming

The windowed offset linear canonical transform (WOLCT) can be identified as a generalization of the windowed linear canonical transform (WLCT). In this paper, we generalize several different uncertainty principles for the WOLCT, including…

Classical Analysis and ODEs · Mathematics 2019-11-07 Wen-Biao Gao , Bing-Zhao Li

In this paper, we prove both of the Titchmarsh theorems associated with Two-Sided Quaternionic Fourier Transform and we conclude about Short-Time Two-Sided Quaternionic Fourier Transform.

Classical Analysis and ODEs · Mathematics 2021-09-21 Hakim Monaim , Said Fahlaoui