Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Convolutions (Mathematics). --- Tauberian theorems.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book gives a complete exposition of the theory of tauberian operators from the very basic results to the most recent advances making emphasis in its applications to Banach space theory. After describing the origins of the subject in the study of summability of series, it presents the general theory for tauberian operators on abstract Banach spaces. The main sources of examples of tauberian operators are described in detail, including the case of operators on spaces of integrable functions.

Tauberian theorems --- Banach spaces --- Operator theory --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Applied Mathematics --- Calculus --- Tauberian theorems. --- Banach spaces. --- Operator theory. --- Mathematics. --- Operator Theory. --- Functional analysis --- Functions of complex variables --- Generalized spaces --- Topology --- Series, Infinite

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Tauberian theorems. --- Summability theory. --- Hardy-Littlewood method. --- Hardy-Littlewood method --- Summability theory --- Tauberian theorems --- 517.4 --- 517.4 Functional determinants. Integral transforms. Operational calculus --- Functional determinants. Integral transforms. Operational calculus --- Series, Infinite --- Sequences (Mathematics) --- Series --- Diophantine analysis --- Equations --- Number theory --- Numerical solutions --- Théorèmes taubériens

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Spectral synthesis

Functional analysis --- Differential equations --- Locally compact Abelian groups --- Spectral synthesis (Mathematics) --- Tauberian theorems --- #KVIV --- #WWIS:STAT --- 517.518.1 --- 517.518.1 Measure. Integration. Differentiation --- Measure. Integration. Differentiation --- Series, Infinite --- Synthesis, Spectral (Mathematics) --- Group theory --- Harmonic analysis --- Spectral theory (Mathematics) --- Compact Abelian groups --- Locally compact groups --- Topological groups --- Spectral synthesis (Mathematics). --- Locally compact Abelian groups. --- Tauberian theorems. --- 517.5 --- Banach, Algèbres de --- Fourier, Analyse de --- Banach, Algèbres de --- Théorèmes taubériens --- 517.5 Theory of functions --- Theory of functions

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

"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"--

Spectral theory (Mathematics) --- Nonselfadjoint operators. --- Laguerre polynomials. --- Partial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theory. --- Operator theory -- Groups and semigroups of linear operators, their generalizations and applications -- Markov semigroups and applications to diffusion processes. --- Approximations and expansions -- Approximations and expansions -- Asymptotic approximations, asymptotic expansions (steepest descent, etc.). --- Probability theory and stochastic processes -- Distribution theory -- Infinitely divisible distributions; stable distributions. --- Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- General harmonic expansions, frames. --- Sequences, series, summability -- Inversion theorems -- Tauberian theorems, general. --- Functions of a complex variable -- Entire and meromorphic functions, and related topics -- Functional equations in the complex domain, iteration and composition of analytic functions. --- Integral transforms, operational calculus -- Integral transforms, operational calculus -- Transforms of special functions.