On the oscillation of differential transforms of eigenfunction expansions

Authors:
C. L. Prather and J. K. Shaw

Journal:
Trans. Amer. Math. Soc. **280** (1983), 187-206

MSC:
Primary 42C15; Secondary 30B50, 34B05

DOI:
https://doi.org/10.1090/S0002-9947-1983-0712255-9

MathSciNet review:
712255

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Abstract: This paper continues the study of Pólya and Wiener, Hille and Szegö into the connections between the oscillation of derivatives of a real function and its analytic character. In the present paper, a Sturm-Liouville operator is applied successively to an infinitely differentiable function which admits a certain eigenfunction expansion. The eigenfunction expansion is assumed to be "conservative", in the sense of Hille. Several theorems are given which link the frequency of oscillation of to the size of the coefficients of , and thus to its analytic character.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1983-0712255-9

Keywords:
Eigenfunction expansion,
iterates of operators,
sign changes

Article copyright:
© Copyright 1983
American Mathematical Society