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Generalized Hilbert matrices and hypergeometric functions

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79 pages
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


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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 Hλ=m+1n+λm,nN
whereλC\ {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
kH1kl2l2π;
Recent generalization to weightedl2-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
kH1kl2l2π;
Recent generalization to weightedl2-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
kH1kl2l2π;
Recent generalization to weightedl2-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
IfλR,Hλinduces a bounded linear operator onl2that is self adjoint.
joint with A. Montes Rodriguez and A. Sarafoleanu
Generalized Hilbert matrices and hypergeometric functions
Its spectrum, and especially the eigenvalue problem
Hλx=µx
have been intensively studied in the 50’s.
More general version of the eigenvalue problem: µCis called alatent rootif there exists a non zero sequence {xn}that satisfies
N Xn+mxn+λ−→µxm. n=0
joint with A. Montes Rodriguez and A. Sarafoleanu
Generalized Hilbert matrices and hypergeometric functions