Generalized Hilbert matrices and hypergeometric functions

Joint With A. Montes Rodriguez And A. Sarafoleanu

Description

Generalized Hilbert matrices and hypergeometric functions joint with A. Montes Rodriguez and A. Sarafoleanu May 30, 2010 joint with A. Montes Rodriguez and A. Sarafoleanu Generalized Hilbert matrices and hypergeometric functions

• recent generalization


• hilbert inequality


• hilbert


• ?h1?l2?l2 ≤


• sarafoleanu generalized


• matrix has


• diamatopoulos - siskakis


• hilbert matrix

Sujets

• David Hilbert
• Hilbert matrix

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 40
• Langue: English

Extrait

Ge

neralized Hilbert hypergeometric

matrices functions

and

joint with A. Montes Rodriguez and A. Sarafoleanu

May 30, 2010

joint with A. Montes Rodriguez and A. Sarafoleanu

Generalized Hilbert matrices and hypergeometric functions

A generalized Hilbert matrix has the form H λ =  m+ 1 n+λ  m,n∈N

whereλ∈C\ {0,−1,−2. . . ,}.

joint with A. Montes Rodriguez and A. Sarafoleanu

∪{0}

Generalized Hilbert matrices and hypergeometric functions

This is a classical Hankel matrix which has attracted a lot of attention. The famous Hilbert inequality

kH 1 k l 2 →l 2 ≤π;

Recent generalization to weightedl 2 -spaces by Diamatopoulos - Siskakis; ”Trick or treats with the Hilbert matrix” by Man-Deun Choi.

joint with A. Montes Rodriguez and A. Sarafoleanu

Generalized Hilbert matrices and hypergeometric functions

This is a classical Hankel matrix which has attracted a lot of attention. The famous Hilbert inequality

kH 1 k l 2 →l 2 ≤π;

Recent generalization to weightedl 2 -spaces by Diamatopoulos - Siskakis; ”Trick or treats with the Hilbert matrix” by Man-Deun Choi.

joint with A. Montes Rodriguez and A. Sarafoleanu

Generalized Hilbert matrices and hypergeometric functions

This is a classical Hankel matrix which has attracted a lot of attention. The famous Hilbert inequality

kH 1 k l 2 →l 2 ≤π;

Recent generalization to weightedl 2 -spaces by Diamatopoulos - Siskakis; ”Trick or treats with the Hilbert matrix” by Man-Deun Choi.

joint with A. Montes Rodriguez and A. Sarafoleanu

Generalized Hilbert matrices and hypergeometric functions

Ifλ∈R,H λ induces a bounded linear operator onl 2 that is self adjoint.

joint with A. Montes Rodriguez and A. Sarafoleanu

Generalized Hilbert matrices and hypergeometric functions

Its spectrum, and especially the eigenvalue problem

H λ x=µx

have been intensively studied in the 50’s.

More general version of the eigenvalue problem: µ∈Cis called alatent rootif there exists a non zero sequence {x n }that satisfies

N X n+m x n +λ −→µx m . n=0

joint with A. Montes Rodriguez and A. Sarafoleanu

Generalized Hilbert matrices and hypergeometric functions