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Author Patie, Pierre, author
Title Spectral expansions of non-self-adjoint generalized laguerre semigroups / Pierre Patie, Mladen Savov
Imprint Providence : American Mathematical Society, [2022]
book jacket
 Mathematics Library  QA320 .P38 2022    AVAILABLE    30340200570277
Descript 1 volume ; 26 cm
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
Series Memoirs of the American Mathematical Society, 0065-9266 ; Volume 272, Number 1336 (sixth of 7 numbers)
Note Includes bibliographical references
"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
Subject Spectral theory (Mathematics)
Nonselfadjoint operators
Laguerre polynomials
Markov processes
Markov Chains
Markov processes. fast (OCoLC)fst01010347
Semigroups. fast (OCoLC)fst01112267
Partial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theory. msc
Operator theory -- Groups and semigroups of linear operators, their generalizations and applications -- Markov semigroups and applications to diffusion processes. msc
Approximations and expansions -- Approximations and expansions -- Asymptotic approximations, asymptotic expansions (steepest descent, etc.). msc
Probability theory and stochastic processes -- Distribution theory -- Infinitely divisible distributions; stable distributions. msc
Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- General harmonic expansions, frames. msc
Sequences, series, summability -- Inversion theorems -- Tauberian theorems, general. msc
Functions of a complex variable -- Entire and meromorphic functions, and related topics -- Functional equations in the complex domain, iteration and composition of analytic functions. msc
Integral transforms, operational calculus -- Integral transforms, operational calculus -- Transforms of special functions. msc
Alt Author Savov, Mladen, author
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