Topic
Shift theorem
About: Shift theorem is a research topic. Over the lifetime, 636 publications have been published within this topic receiving 11484 citations.
Papers published on a yearly basis
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Papers
Book•
31 Dec 1934
TL;DR: In this article, a generalized harmonic analysis in the complex domain of random functions has been proposed, based on Szasz's theorem and a class of singular integral equations of the exponential type.
Abstract: Introduction Quasi-analytic functions Szasz's theorem Certain integral expansions A class of singular integral equations Entire functions of the exponential type The closure of sets of complex exponential functions Non-harmonic Fourier series and a gap theorem Generalized harmonic analysis in the complex domain The harmonic analysis of random functions Bibliography Index.
1,704 citations
TL;DR: In this article, a Lieb-Robinson bound for the group velocity of a large class of discrete quantum systems is given, which can be used to prove that a non-vanishing spectral gap implies exponential clustering in the ground state of such systems.
Abstract: We give a Lieb-Robinson bound for the group velocity of a large class of discrete quantum systems which can be used to prove that a non-vanishing spectral gap implies exponential clustering in the ground state of such systems.
555 citations
TL;DR: The result is used to show that input-to-state stabilizability for nonlinear finite-dimensional control systems is robust, in an appropriate sense, to small time delays at the input.
Abstract: A Razumikhin-type theorem that guarantees input-to-state stability for functional differential equations with disturbances is established using the nonlinear small-gain theorem. The result is used to show that input-to-state stabilizability for nonlinear finite-dimensional control systems is robust, in an appropriate sense, to small time delays at the input. Also, relaxed Razumikhin-type conditions guaranteeing global asymptotic stability for differential difference equations are given.
485 citations
TL;DR: The Stone-Weierstrass theorem is reviewed, and a modified logistic network satisfying the theorem is proposed as an alternative to commonly used networks based on logistic squashing functions.
Abstract: The Stone-Weierstrass theorem and its terminology are reviewed, and neural network architectures based on this theorem are presented. Specifically, exponential functions, polynomials, partial fractions, and Boolean functions are used to create networks capable of approximating arbitrary bounded measurable functions. A modified logistic network satisfying the theorem is proposed as an alternative to commonly used networks based on logistic squashing functions. >
405 citations
381 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2024 | 2 |
| 2023 | 3 |
| 2022 | 1 |
| 2021 | 1 |
| 2018 | 4 |
| 2017 | 15 |