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Lectures on Hermite and Laguerre expansions / by Sundaram Thangavelu
| Lectures on Hermite and Laguerre expansions / by Sundaram Thangavelu |
| Autore | Thangavelu, Sundaram |
| Pubbl/distr/stampa | Princeton, N.J. : Princeton University Press, 1993 |
| Descrizione fisica | xv, 195 p. : ill. ; 24 cm. |
| Disciplina | 515.5 |
| Collana | Mathematical notes ; 42 |
| Soggetto topico |
Hermite polynomials
Laguerre polynomials Representations of groups |
| ISBN | 0691000484 |
| Classificazione |
AMS 42C10
QA404.5.T37 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001065959707536 |
Thangavelu, Sundaram
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| Princeton, N.J. : Princeton University Press, 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups
| Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups |
| Autore | Patie Pierre |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2021 |
| Descrizione fisica | 1 online resource (196 pages) |
| Disciplina | 515/.7222 |
| Altri autori (Persone) | SavovMladen |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
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 |
| ISBN |
9781470467524
1470467526 |
| Classificazione | 35P0547D0741A6060E0742C1540E0530D0544A20 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title page -- Acknowledgments -- Chapter 1. Introduction and main results -- 1.1. Characterization and properties of gL semigroups -- 1.2. Definition and properties of subsets of \Ne -- 1.3. Eigenvalue expansion and regularity of the gL semigroups -- 1.4. Convergence to equilibrium -- 1.5. Hilbert sequences and spectrum -- 1.6. Plan of the paper -- 1.7. Notation, conventions and general facts -- Chapter 2. Strategy of proofs and auxiliary results -- 2.1. Outline of our methodology -- 2.2. Proof of Theorem ??? (???) -- 2.3. Additional basic facts on gL semigroups -- Chapter 3. Examples -- Chapter 4. New developments in the theory of Bernstein functions -- 4.1. Review and basic properties of Bernstein functions -- 4.2. Products of Bernstein functions: new examples -- 4.3. Useful estimates of Bernstein functions on \C₊ -- Chapter 5. Fine properties of the density of the invariant measure -- 5.1. A connection with remarkable self-decomposable variables -- 5.2. Fine distributional properties of _{ } -- 5.3. Proof of Theorem ??? (???) -- 5.4. Small asymptotic behaviour of \nuh and of its successive derivatives -- 5.5. Proof of Theorem ??? -- 5.6. Proof of Theorem ??? -- 5.7. End of proof of Theorem ??? -- Chapter 6. Bernstein-Weierstrass products and Mellin transforms -- 6.1. Exponential functional of subordinators -- 6.2. The functional equations (???) and (???) on \R₊ -- 6.3. Proof of Theorem ??? -- 6.4. Proof of Proposition 6.1.2 -- 6.5. Proof of Theorem ??? (???): Bounds for ᵩ -- 6.6. Large asymptotic behaviours of ᵩ along imaginary lines -- 6.7. Proof of Theorem ??? (???) -- 6.8. Proof of Theorem 6.0.2 (2b): Examples of large asymptotic estimates of | ᵩ| -- Chapter 7. Intertwining relations and a set of eigenfunctions -- 7.1. Proof of Theorem ??? -- 7.2. End of the proof of the intertwining relation (7.3).
7.3. Proofs of Theorem ??? (???) and (???) -- 7.4. Proof of the uniqueness of the invariant measure -- 7.5. Proof of Theorem ??? -- Chapter 8. Co-eigenfunctions: existence and characterization -- 8.1. Mellin convolution equations: distributional and classical solutions -- 8.2. Existence of co-eigenfunctions: Proof of Theorem ??? -- 8.3. The case ∈\Ne_{∞,∞}. -- 8.4. The case ∈\Ne_{∞}∖\Nii -- 8.5. The case ∈\Ne^{ }_{∞}. -- Chapter 9. Uniform and norms estimates of the co-eigenfunctions -- 9.1. Proof of Theorem 2.1.5 (1) via a classical saddle point method -- 9.2. Proof of Theorem 2.1.5 (2) via the asymptotic behaviour of zeros of the derivatives of -- 9.3. Proof of Theorem ??? (???) through Phragmén-Lindelöf principle -- Chapter 10. The concept of reference semigroups: \Lnu-norm estimates and completeness of the set of co-eigenfunctions -- 10.1. Estimates for the \lnu norm of \nun -- 10.2. Completeness of (\nun)_{ ≥0} in \lnu -- Chapter 11. Hilbert sequences, intertwining and spectrum -- 11.1. Proof of Theorem ??? -- Chapter 12. Proof of Theorems ???, ??? and ??? -- 12.1. Proof of Theorem 1.3.1 (2) -- 12.2. Proof of Theorem ??? (???) -- 12.3. Heat kernel expansion -- 12.4. Expansion of the adjoint semigroup: Proof of Theorem ??? -- 12.5. Proof of of Theorem ???: Rate of convergence to equilibrium -- Bibliography -- Back Cover. |
| Record Nr. | UNINA-9910972392703321 |
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Patie Pierre
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| Providence : , : American Mathematical Society, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Soggetto topico
-
Laguerre polynomials
(2)
- Approximations and expansions -- Approximations and expansions -- Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (1)
- Functions of a complex variable -- Entire and meromorphic functions, and related topics -- Functional equations in the complex domain, iteration and composition of analytic functions (1)
- Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- General harmonic expansions, frames (1)
- Hermite polynomials (1)