Special functions as subordinated semigroups on the real line. (English) Zbl 1368.33008
Summary: We give examples of convolution semigroups on the positive half-line and on the real line. Such semigroups are expressed in terms of special functions which arise in classical differential equations.
MSC:
33C80 | Connections of hypergeometric functions with groups and algebras, and related topics |
33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
33C15 | Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\) |
33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
34A30 | Linear ordinary differential equations and systems |
46J15 | Banach algebras of differentiable or analytic functions, \(H^p\)-spaces |
46N20 | Applications of functional analysis to differential and integral equations |
47D03 | Groups and semigroups of linear operators |
Keywords:
convolution semigroups; special functions; Sobolev algebras; confluent hypergeometric functions; Hankel functions; modified Bessel functions; McDonald functions; Hermite functions; Poisson semigroup; Gauss-Weierstrass semigroup; fractional semigroup; backwards heat semigroupReferences:
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