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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Hermite series as boundary values


Author: G. G. Walter
Journal: Trans. Amer. Math. Soc. 218 (1976), 155-171
MSC: Primary 31A20
DOI: https://doi.org/10.1090/S0002-9947-1976-0402081-9
MathSciNet review: 0402081
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Abstract: The relations between Hermite series expansions of functions and tempered distributions on the real axis and holomorphic or harmonic functions or generalizations of them in the upper half plane are studied. The Hermite series expansions of $ {H^2}$ functions are characterized in terms of their coefficients. Series of analytic representations of Hermite functions, series of Hermite functions of the second kind, and combined series of Hermite functions of the first and second kind are investigated. The functions to which these series converge in the upper half plane are shown to approach (in various ways) the distributions or functions whose Hermite series have the same coefficients.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0402081-9
Keywords: Harmonic oscillator, Hermite functions, harmonic functions, tempered distributions, boundary values
Article copyright: © Copyright 1976 American Mathematical Society

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