Exact propagators for some degenerate hyperbolic operators

Richard Beals; Yakar Kannai

doi:10.1007/s11512-006-0018-5

Exact propagators for some degenerate hyperbolic operators

Richard Beals, Yakar Kannai

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Exact propagators are obtained for the degenerate second order hyperbolic operators ∂_t² - t^2l Δ_x, l=1, 2, ..., by analytic continuation from the degenerate elliptic operators ∂_t² + t^2l Δ_x. The partial Fourier transforms are also obtained in closed form, leading to integral transform formulas for certain combinations of Bessel functions and modified Bessel functions.

Original language	English
Pages (from-to)	191-209
Number of pages	19
Journal	Arkiv for Matematik
Volume	44
Issue number	2
DOIs	https://doi.org/10.1007/s11512-006-0018-5
State	Published - Oct 2006
Externally published	Yes

Bibliographical note

Funding Information:
Acknowledgement. Research of the first author was supported in by part by the National Science Foundation, DMS Grant 9800605.

Funding

Acknowledgement. Research of the first author was supported in by part by the National Science Foundation, DMS Grant 9800605.

Funders	Funder number
Division of Mathematical Sciences	9800605
National Science Foundation

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10.1007/s11512-006-0018-5

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abstract = "Exact propagators are obtained for the degenerate second order hyperbolic operators ∂t2 - t2l Δx, l=1, 2, ..., by analytic continuation from the degenerate elliptic operators ∂t2 + t2l Δx. The partial Fourier transforms are also obtained in closed form, leading to integral transform formulas for certain combinations of Bessel functions and modified Bessel functions.",

author = "Richard Beals and Yakar Kannai",

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AB - Exact propagators are obtained for the degenerate second order hyperbolic operators ∂t2 - t2l Δx, l=1, 2, ..., by analytic continuation from the degenerate elliptic operators ∂t2 + t2l Δx. The partial Fourier transforms are also obtained in closed form, leading to integral transform formulas for certain combinations of Bessel functions and modified Bessel functions.

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Exact propagators for some degenerate hyperbolic operators

Abstract

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