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020 a| 9781470449360q| (paperback);

020 z| 9781470467524q| (epub);

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100 1 a| Patie, Pierre.?| UNAUTHORIZED;

245 10 a| Spectral expansions of non-self-adjoint generalized laguerre semigroupsh| [electronic resource] /c| Pierre Patie, Mladen Savov.;

260 a| Providence :b| American Mathematical Society,c| [2021];

300 a| vii, 182 pages ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Volume 272, Number 1336 (sixth of 7 numbers);

504 a| Includes bibliographical references.;

506 a| Available only to authorized users.;

520 a| "We provide the spectral expansion in a weighted Hilbert space of a substantial class of invariant non-self-adjoint and non-local Markov operators which appear in limit theorems for positive-valued Markov processes. We show that this class is in bijection with a subset of negative definite functions and we name it the class of generalized Laguerre semigroups. Our approach, which goes beyond the framework of perturbation theory, is based on an in-depth and original analysis of an intertwining relation that we establish between this class and a self-adjoint Markov semigroup, whose spectral expansion is expressed in terms of the classical Laguerre polynomials. As a by-product, we derive smoothness properties for the solution to the associated Cauchy problem as well as for the heat kernel. Our methodology also reveals a variety of possible decays, including the hypocoercivity type phenomena, for the speed of convergence to equilibrium for this class and enables us to provide an interpretation of these in terms of the rate of growth of the weighted Hilbert space norms of the spectral projections. Depending on the analytic properties of the aforementioned negative definite functions, we are led to implement several strategies, which require new developments in a variety of contexts, to derive precise upper bounds for these norms"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Spectral theory (Mathematics)=| ^A21221;

650 0 a| Nonselfadjoint operators.=| ^A169312;

650 0 a| Laguerre polynomials.=| ^A215328;

650 7 a| Partial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theory.2| msc;

650 7 a| Operator theory -- Groups and semigroups of linear operators, their generalizations and applications -- Markov semigroups and applications to diffusion processes.2| msc;

650 7 a| Approximations and expansions -- Approximations and expansions -- Asymptotic approximations, asymptotic expansions (steepest descent, etc.).2| msc;

650 7 a| Probability theory and stochastic processes -- Distribution theory -- Infinitely divisible distributions; stable distributions.2| msc;

650 7 a| Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- General harmonic expansions, frames.2| msc;

650 7 a| Sequences, series, summability -- Inversion theorems -- Tauberian theorems, general.2| msc;

650 7 a| Functions of a complex variable -- Entire and meromorphic functions, and related topics -- Functional equations in the complex domain, iteration and composition of analytic functions.2| msc;

650 7 a| Integral transforms, operational calculus -- Integral transforms, operational calculus -- Transforms of special functions.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Savov, Mladen.?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6798079;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6516474-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 1/14/2025x| EBOOKz| JERESOURCE;

Spectral expansions of non-self-adjoint generalized laguerre semigroups / Pierre Patie, Mladen Savov.

Author/creator	Patie, Pierre
Other author	Savov, Mladen.
Format	Electronic
Publication Info	Providence : American Mathematical Society, [2021]
Description	vii, 182 pages ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Spectral theory (Mathematics) Nonselfadjoint operators. Laguerre polynomials.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; Volume 272, Number 1336 (sixth of 7 numbers)
Abstract	"We provide the spectral expansion in a weighted Hilbert space of a substantial class of invariant non-self-adjoint and non-local Markov operators which appear in limit theorems for positive-valued Markov processes. We show that this class is in bijection with a subset of negative definite functions and we name it the class of generalized Laguerre semigroups. Our approach, which goes beyond the framework of perturbation theory, is based on an in-depth and original analysis of an intertwining relation that we establish between this class and a self-adjoint Markov semigroup, whose spectral expansion is expressed in terms of the classical Laguerre polynomials. As a by-product, we derive smoothness properties for the solution to the associated Cauchy problem as well as for the heat kernel. Our methodology also reveals a variety of possible decays, including the hypocoercivity type phenomena, for the speed of convergence to equilibrium for this class and enables us to provide an interpretation of these in terms of the rate of growth of the weighted Hilbert space norms of the spectral projections. Depending on the analytic properties of the aforementioned negative definite functions, we are led to implement several strategies, which require new developments in a variety of contexts, to derive precise upper bounds for these norms"-- Provided by publisher.
Bibliography note	Includes bibliographical references.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022008015
ISBN	9781470449360 (paperback)
ISBN	(epub)

Spectral expansions of non-self-adjoint generalized laguerre semigroups / Pierre Patie, Mladen Savov.

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