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Harmonic Analysis and Representation Commons™
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Articles 1 - 3 of 3
Full-Text Articles in Harmonic Analysis and Representation
Interpolation And Sampling In Analytic Tent Spaces, Caleb Parks
Interpolation And Sampling In Analytic Tent Spaces, Caleb Parks
Graduate Theses and Dissertations
Introduced by Coifman, Meyer, and Stein, the tent spaces have seen wide applications in harmonic analysis. Their analytic cousins have seen some applications involving the derivatives of Hardy space functions. Moreover, the tent spaces have been a recent focus of research. We introduce the concept of interpolating and sampling sequences for analytic tent spaces analogously to the same concepts for Bergman spaces. We then characterize such sequences in terms of Seip's upper and lower uniform density. We accomplish this by exploiting a kind of Mobius invariance for the tent spaces.
A Course In Harmonic Analysis, Jason Murphy
A Course In Harmonic Analysis, Jason Murphy
AOER Course Materials
These notes were written to accompany the courses Math 6461 and Math 6462 (Harmonic Analysis I and II) at Missouri University of Science & Technology during the 2018-2019 academic year. The goal of these notes is to provide an introduction to a range of topics and techniques in harmonic analysis, covering material that is interesting not only to students of pure mathematics, but also to those interested in applications in computer science, engineering, physics, and so on.
On The Lp-Error Of Approximation Of Bivariate Functions By Harmonic Splines, Yuliya Babenko, Tatyana Leskevich
On The Lp-Error Of Approximation Of Bivariate Functions By Harmonic Splines, Yuliya Babenko, Tatyana Leskevich
Faculty Articles
Interpolation by various types of splines is the standard procedure in many applications. In this paper we discuss harmonic spline “interpolation” (on the lines of a grid) as an alternative to polynomial spline interpolation (at vertices of a grid). We will discuss some advantages and drawbacks of this approach and present the asymptotics of the Lp-error for adaptive approximation by harmonic splines.