Superoscillations and Analytic Extension in Schur Analysis

Daniel Alpay; Fabrizio Colombo; Irene Sabadini

doi:10.1007/s00041-020-09808-9

Superoscillations and Analytic Extension in Schur Analysis

Daniel Alpay, Fabrizio Colombo, Irene Sabadini

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

2 Scopus citations

Abstract

We give applications of the theory of superoscillations to various questions, namely extension of positive definite functions, interpolation of polynomials and also of R-functions; we also discuss possible applications to signal theory and prediction theory of stationary stochastic processes. In all cases, we give a constructive procedure, by way of a limiting process, to get the required results.

Original language	English
Article number	28
Journal	Journal of Fourier Analysis and Applications
Volume	27
Issue number	2
DOIs	https://doi.org/10.1007/s00041-020-09808-9
State	Published - 1 Apr 2021
Externally published	Yes

Keywords

Analytic extension
Stationary stochastic processes
Superoscillations

ASJC Scopus subject areas

Analysis
Mathematics (all)
Applied Mathematics

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10.1007/s00041-020-09808-9

Cite this

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title = "Superoscillations and Analytic Extension in Schur Analysis",

abstract = "We give applications of the theory of superoscillations to various questions, namely extension of positive definite functions, interpolation of polynomials and also of R-functions; we also discuss possible applications to signal theory and prediction theory of stationary stochastic processes. In all cases, we give a constructive procedure, by way of a limiting process, to get the required results.",

keywords = "Analytic extension, Stationary stochastic processes, Superoscillations",

author = "Daniel Alpay and Fabrizio Colombo and Irene Sabadini",

note = "Funding Information: Open Access funding provided by Politecnico di Milano. The authors are grateful to the referee for the useful comments. Publisher Copyright: {\textcopyright} 2021, The Author(s).",

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AU - Colombo, Fabrizio

AU - Sabadini, Irene

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N2 - We give applications of the theory of superoscillations to various questions, namely extension of positive definite functions, interpolation of polynomials and also of R-functions; we also discuss possible applications to signal theory and prediction theory of stationary stochastic processes. In all cases, we give a constructive procedure, by way of a limiting process, to get the required results.

AB - We give applications of the theory of superoscillations to various questions, namely extension of positive definite functions, interpolation of polynomials and also of R-functions; we also discuss possible applications to signal theory and prediction theory of stationary stochastic processes. In all cases, we give a constructive procedure, by way of a limiting process, to get the required results.

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KW - Stationary stochastic processes

KW - Superoscillations

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Superoscillations and Analytic Extension in Schur Analysis

Abstract

Keywords

ASJC Scopus subject areas

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