Documents  Critères de recherche : "Orthogonal polynomials" | enregistrements trouvés : 49

ISBN 978-3-540-19489-7

Lecture notes in mathematics , 1329

Localisation : Collection 1er étage

polynome orthogonaux

33A65 ; 42C05

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IMACS annals on computing and applied mathematics , 0009

Localisation : Colloque 1er étage (ERIC)

calcul informatique # mathématique appliquée # mathématique discrète # polynome orthogonal

33C45

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ISBN 978-0-8176-6137-3

International series of numerical mathematics , 0131

Localisation : Colloque 1er étage (OBER)

analyse numérique # application # approximation numérique # calcul # intégration numérique # polynome orthogonal # système algébrique linéaire

65-06

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- 249 p.
ISBN 978-3-540-40375-3

Lecture notes in mathematics , 1817

Localisation : Collection 1er étage

fonction spéciale # polynôme orthogonal # calcul formel # opérateur de Dunkl # énumération # asymptotique exponentielle # développement asymptotique

33-01 ; 33F10 ; 68W30 ; 33C80 ; 22E47 ; 05A15 ; 34E05 ; 42C05 ; 30E25 ; 41A60 ; 33C52 ; 34M40

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- 773 p.
ISBN 978-981-270-643-0

Localisation : Colloque 1er étage (MUNI)

équations fonctionnelles # fonctions particulières # systèmes dynamiques # théorie ergodique # analyse de Fourier

39-06 ; 33-06 ; 37-06 ; 42-06 ; 00B25

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- 948 p.
ISBN 978-0-8218-4249-2

Proceedings of symposia in pure mathematics , 0076

Localisation : Collection 1er étage

EDO # problème inverse # théorie spectrale # opérateur de Dirac # opérateur de Schrödinger # théorie ergodique multiplicative # fonction orthogonale # fonction polynomiale # opérateur linéaire # spectre # résolvante # opérateur de Jacobi # opérateur aléatoire # opérateurs dans la théorie quantique

34A55 ; 34L05 ; 34L40 ; 37H15 ; 42C05 ; 47A10 ; 47B36 ; 60H25 ; 81Q10

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- v; 218 p.
ISBN 978-0-8218-4650-6

Contemporary mathematics , 0471

Localisation : Collection 1er étage

fonction spéciale # polynômes orthogonaux # analyse asymptotique # application conforma # équation différentielle # fonction élliptique # calcul fractionnel # série hypergéométrique # série q-hypergéométrique # onde non-linéaire # fonction théta

33-06 ; 42-06 ; 00B25

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- x, 298 p.
ISBN 978-0-8218-4803-6

Contemporary mathematics , 0507

Localisation : Collection 1er étage

fonction spéciale # polygone orthogonale

15A52 ; 26C10 ; 30E10 ; 31A15 ; 31C15 ; 33C47 ; 41A20 ; 42C05 ; 44A60 ; 65D32

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- viii, 231 p.
ISBN 978-0-8218-4886-9

Contemporary mathematics , 0509

Localisation : Collection 1er étage

polynômes othogonaux # système dynamique intégrable # théorie de Galois différentielle # groupe de Lie # singularités # 16ème problème de Hilbert

05C20 ; 12H05 ; 14E20 ; 14L99 ; 14M15 ; 20C20 ; 30C45 ; 33C50 ; 33D45 ; 34A26 ; 34C07 ; 34C08 ; 34M15 ; 35C05 ; 41A60 ; 42C05 ; 46E25 ; 53C15 ; 54C40

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- x-254 p.
ISBN 978-0-8218-6896-6

Contemporary mathematics , 0578

Localisation : Collection 1er étage

fonction d'une variable complexe

00B25 ; 33-06 ; 30-06 ; 41-06 ; 42-06 ; 33C45 ; 33C47 ; 30E10 ; 41A20 ; 42C10

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Mathematical Physics;Probability and Statistics

For the commonly studied Hermitian random matrix models there exist tridiagonal matrix models with the same eigenvalue distribution and the same spectral measure $v_{n}$ at the vector $e_{1}$. These tridiagonal matrices give recurrence coefficients that can be used to build the family of random polynomials that are orthogonal with respect to νn. A similar bijection between spectral data and recurrence coefficients also holds for the Unitary ensembles. This time in stead of obtaining a tridiagonal matrix you obtain a sequence $\left \{ \alpha _{k} \right \}_{k=0}^{n-1}$ Szegö coefficients. The random orthogonal polynomials that are generated by this process may then be used to study properties of the original eigenvalue process.
These techniques may be used not just in the classical cases, but also in the more general case of $\beta $-ensembles. I will discuss various ways that orthogonal polynomials techniques may be applied including to show convergence of the Circular $\beta $-ensemble to $Sine_{\beta }$. I will finish by discussing a result on the maximum deviation of the counting function of Sineβ from it expected value. This is related to studying the phases of associated random orthogonal polynomials. For the commonly studied Hermitian random matrix models there exist tridiagonal matrix models with the same eigenvalue distribution and the same spectral measure $v_{n}$ at the vector $e_{1}$. These tridiagonal matrices give recurrence coefficients that can be used to build the family of random polynomials that are orthogonal with respect to νn. A similar bijection between spectral data and recurrence coefficients also holds for the Unitary ...

60B20 ; 15B52

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Geometry;Mathematical Physics

We establish a new connection between moments of n×n random matrices $X_{n}$ and hypergeometric orthogonal polynomials. Specifically, we consider moments $\mathbb{E}\mathrm{Tr} X_n^{-s}$ as a function of the complex variable $s\in\mathbb{C}$, whose analytic structure we describe completely. We discover several remarkable features, including a reflection symmetry (or functional equation), zeros on a critical line in the complex plane, and orthogonality relations. In each of the classical ensembles of random matrix theory (Gaussian, Laguerre, Jacobi) we characterise the moments in terms of the Askey scheme of hypergeometric orthogonal polynomials. We also calculate the leading order n→∞ asymptotics of the moments and discuss their symmetries and zeroes. We discuss aspects of these phenomena beyond the random matrix setting, including the Mellin transform of products and Wronskians of pairs of classical orthogonal polynomials. When the random matrix model has orthogonal or symplectic symmetry, we obtain a new duality formula relating their moments to hypergeometric orthogonal polynomials. This is work in collaboration with Fabio Cunden, Neil O' Connell and Nick Simm. We establish a new connection between moments of n×n random matrices $X_{n}$ and hypergeometric orthogonal polynomials. Specifically, we consider moments $\mathbb{E}\mathrm{Tr} X_n^{-s}$ as a function of the complex variable $s\in\mathbb{C}$, whose analytic structure we describe completely. We discover several remarkable features, including a reflection symmetry (or functional equation), zeros on a critical line in the complex plane, and ...

15B52 ; 05E05 ; 33C45

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ISBN 978-0-8218-2301-9

Memoirs of the american mathematical society , 0300

Localisation : Collection 1er étage

30B70 ; 30E05 ; 33A65

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ISBN 978-0-8218-2321-7

Memoirs of the american mathematical society , 0319

Localisation : Collection 1er étage

05A17 ; 05A19 ; 10A45 ; 26Axx ; 26C10

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- 201 p.
ISBN 978-3-540-18023-4

Lecture notes in mathematics , 1265

Localisation : Collection 1er étage

polynomes orthogonaux # théorie asymptotique

42C05

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- xii; 179 p.
ISBN 978-1-108-44194-0

Australian mathematical society lecture series , 0027

Localisation : Ouvrage RdC (VANA)

équation de Painlevé # polynôme orthogonal

33-01 ; 33C45 ; 33C47 ; 33E17

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- 250 p.
ISBN 978-0-521-41534-7

Encyclopedia of mathematics and its applications , 0043

Localisation : Collection 1er étage

approximant de Pade # fonction de Markov # plan complexe # polynôme orthogonal # polynôme orthonormal # théorie de l'approximation # théorie du potentiel # transformée de Cauchy pour les mesures

26C10 ; 33A65 ; 33C45

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- 250 p.
ISBN 978-3-7643-1100-1

I.S.N.M. , 0050

Localisation : Ouvrage RdC (BREZ)

analyse de Fourier non trigonométrique # approximation de type Padé # polynome orthogonal général

41A21 ; 42-XX ; 42C05 ; 42Cxx

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- 294 p.

Localisation : Ouvrage RdC (FREU)

convergence de série de polynôme orthogonal # interpolation # nombre de Christoffel # polynôme orthogonal # problème du moment # procédé de quadrature

30C30 ; 30E05 ; 33C25 ; 42A70 ; 42C15

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