On support properties of Lp-functions and their Fourier transforms
W.O Amrein,A.M Berthier +1 more
TLDR
In this article, the authors give a criterion for the intersection of two projections in Hilbert space to be a projection of finite-dimensional range, which is applied to Schrodinger operators in L2(Rn) and to the problem of determining whether there are functions f and its Fourier transform having prescribed support.About:
This article is published in Journal of Functional Analysis.The article was published on 1977-03-01 and is currently open access. It has received 131 citations till now. The article focuses on the topics: Fourier inversion theorem & Multiplier (Fourier analysis).read more
Citations
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Journal ArticleDOI
Uncertainty principles and signal recovery
David L. Donoho,Philip B. Stark +1 more
TL;DR: In this article, the uncertainty principle can be generalized to cases where the sets of concentration are not intervals, and generalizations explain interesting phenomena in signal recovery problems where there is an interplay of missing data, sparsity, and bandlimiting.
Journal ArticleDOI
The Uncertainty Principle: A Mathematical Survey
Gerald B. Folland,Alladi Sitaram +1 more
TL;DR: The authors survey various mathematical aspects of the uncertainty principle, including Heisenberg inequality and its variants, local uncertainty inequalities, logarithmic uncertainty inequalities and results relating to Wigner distributions, qualitative uncertainty principles, theorems on approximate concentration, and decompositions of phase space.
Book
Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control
Steven L. Brunton,J. Nathan Kutz +1 more
TL;DR: In this paper, the authors bring together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science, and highlight many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy.
Journal ArticleDOI
Quantum designs: foundations of a noncommutative design theory
TL;DR: In this paper, a translation of a German-written PhD thesis from 1999 has been translated to regular affine quantum designs, which are sets of orthogonal projection matrices in finite(b)-dimensional Hilbert spaces.
Journal ArticleDOI
On Fourier transforms of functions supported on sets of finite Lebesgue measure
TL;DR: In this paper, the mesures de Haar and Lebesgue sur R n resp. R n are denotent, i.e., m(A) < ∞ and m(B) <∞⇒f=0 a.e.
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Book
Introduction to Fourier Analysis on Euclidean Spaces.
Elias M. Stein,Guido Weiss +1 more
TL;DR: In this paper, the authors present a unified treatment of basic topics that arise in Fourier analysis, and illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations.
Journal ArticleDOI
Uniqueness of the self-adjoint extension of singular elliptic differential operators
Teruo Ikebe,Tosio Kato +1 more
Book ChapterDOI
The quantum probability calculus
TL;DR: In fact most of the physical interpretation of the formalism of quantum mechanics is expressed in terms of probability statements as discussed by the authors, and most of these statements are expressed in probability calculus, not quantum mechanics.