Difference Sturm-Liouville problems in the imaginary direction

DOI10.4171/JST/44zbMath1277.39014arXiv1104.1936MaRDI QIDQ361716

Yuriĭ A. Neretin

Publication date: 19 August 2013

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.1936

zbMATH Keywords

difference operatorsSturm-Liouville problemspectral decompositionKontorovich-Lebedev transformself-adjoint operatorsself-adjoint extensiondefect indicesindex hypergeometric transforminverse Wimp transformWhittaker kernel

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Integral transforms of special functions (44A20) Integral operators (47G10) Discrete version of topics in analysis (39A12) Difference operators (39A70) Classical hypergeometric functions, ({}_2F_1) (33C05) Linear difference operators (47B39) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (5)

The Fourier transform on the group \(\mathrm{GL}_2(\mathbb{R})\) and the action of the overalgebra \(\mathfrak{gl}_4\) ⋮ A pair of commuting hypergeometric operators on the complex plane and bispectrality ⋮ Restriction of representations of \(\mathrm{GL}(n + 1, \mathbb{C})\) to \(\mathrm{GL}(n, \mathbb{C})\) and action of the Lie overalgebra ⋮ Fourier transform on the Lobachevsky plane and operational calculus ⋮ On a ℂ²-valued integral index transform and bilateral hypergeometric series

Cites Work

• Bernoulli and Euler numbers and orthogonal polynomials
• A new proof of a Paley-Wiener type theorem for the Jacobi transform
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• A Set of Hypergeometric Orthogonal Polynomials
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