Topic
Differential operator
About: Differential operator is a research topic. Over the lifetime, 10274 publications have been published within this topic receiving 154391 citations.
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Book•
2 Dec 2010
TL;DR: In this paper, the existence and uniqueness results for Riemann-Liouville Fractional Differential Equations are presented. But they do not cover the special cases of fractional calculus.
Abstract: Fundamentals of Fractional Calculus.- Riemann-Liouville Differential and Integral Operators.- Caputo's Approach.- Mittag-Leffler Functions.- Theory of Fractional Differential Equations.- Existence and Uniqueness Results for Riemann-Liouville Fractional Differential Equations.- Single-Term Caputo Fractional Differential Equations: Basic Theory and Fundamental Results.- Single-Term Caputo Fractional Differential Equations: Advanced Results for Special Cases.- Multi-Term Caputo Fractional Differential Equations.
2,806 citations
TL;DR: In this article, the BakerHausdorff formula for non-commuting variables is proved in Section I1 of the present paper together with some applications which concern the addition theorem of the exponential function for noncommuting variable.
Abstract: The present investigation was stimulated by a recent paper of K. 0. Friedrichs 113, who arrived at some purely algebraic problems in connection with the theory of linear operators in quantum mechanics. In particuIar, Friedrichs used a theorem by which the Lie elements in a free associative ring can be characterized. This theorem is proved in Section I1 of the present paper together with some applications which concern the addition theorem of the exponential function for non-commuting variables, the so-called BakerHausdorff formula. Section I contains some algebraic preliminaries. It is of a purely expository character and so is part of Section 111. Otherwise, Section 111 deals with the following problem, also considered by Friedrichs: Let A( t ) be a linear operator depending on a real variable 1. Let Y(t) be a second operator satisfying the differential equation
2,657 citations
TL;DR: In this paper, the authors derived analogues for the Airy kernel of the following properties of the sine kernel: the completely integrable system of P.D.E., the expression of the Fredholm determinant in terms of a Painleve transcendent, the existence of a commuting differential operator, and the fact that this operator can be used in the derivation of asymptotics, for generaln, of the probability that an interval contains preciselyn eigenvalues.
Abstract: Scaling level-spacing distribution functions in the “bulk of the spectrum” in random matrix models ofN×N hermitian matrices and then going to the limitN→∞ leads to the Fredholm determinant of thesine kernel sinπ(x−y)/π(x−y). Similarly a scaling limit at the “edge of the spectrum” leads to theAiry kernel [Ai(x)Ai(y)−Ai′(x)Ai(y)]/(x−y). In this paper we derive analogues for this Airy kernel of the following properties of the sine kernel: the completely integrable system of P.D.E.'s found by Jimbo, Miwa, Mori, and Sato; the expression, in the case of a single interval, of the Fredholm determinant in terms of a Painleve transcendent; the existence of a commuting differential operator; and the fact that this operator can be used in the derivation of asymptotics, for generaln, of the probability that an interval contains preciselyn eigenvalues.
2,197 citations
1 Jan 2005
TL;DR: In this article, the authors introduce pseudospectra and non-normal matrices, and describe the behavior of nonsymmetric eigenproblems in non-hermitian systems.
Abstract: spectra and pseudospectra springerlink. spectra and pseudospectra the behavior of nonnormal. spectra and pseudospectra the behavior of nonnormal. spectra and pseudospectra the behavior of nonnormal. on n ? pseudospectra of operators on banach spaces. phd course on pseudospectra aalb universitet. nonhermitian systems and pseudospectra. spectra and pseudospectra the behavior of nonnormal. spectra and pseudospectra the behavior of nonnormal. pseudospectrum scholarpedia. spectra and pseudospectra the behavior of nonnormal. spectra and pseudospectra the behavior of nonnormal. customer reviews spectra and pseudospectra. spectra and pseudospectra request pdf. an introduction to pseudo spectra and non normal matrices. spectra and pseudospectra gbv. pseudospectrum. spectra and pseudospectra the behavior of nonnormal. ???? spectra and pseudospectra the behavior of nonnormal. spectra and pseudospectra the behavior of nonnormal. mark embree lloyd n trefethen abebooks. spectra and pseudospectra the behavior of nonnormal. eigtool a graphical tool for nonsymmetric eigenproblems. spectra and pseudospectra the behavior of nonnormal. universality of non normality in real arxiv vanity. spectra and pseudospectra lloyd n trefethen mark embree. spectra and pseudospectra the behavior of nonnormal. pseudospectra and nonnormal dynamical systems. booksavages. review of spectra and pseudospectra the behavior of. spectra pseudospectra and localization for random. spectra and pseudospectra of block toeplitz matrices. lecture notes on spectra and pseudospectra of matrices and. structure and dynamical behavior of non normal networks. lecture 2 nonnormality and pseudospectra. spectra and pseudospectra the behavior of nonnormal. numerical range for some plex upper triangular matrices. spectra and pseudospectra the behavior of nonnormal. spectra and pseudospectra the behavior of nonnormal. mark embree virginia tech. spectra and pseudospectra princeton university press. bookask?????? ??????????. spectra and pseudospectra the behavior of nonnormal. pseudospectra and inverse pseudospectra springerlink. review of spectra and pseudospectra the behavior of. nick trefethen. pseudospectrum mathematical garden
1,817 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 76 |
| 2024 | 125 |
| 2023 | 316 |
| 2022 | 613 |
| 2021 | 516 |