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October 2012 Representing and interpolating sequences on parabolic Bloch type spaces
Yôsuke HISHIKAWA, Masahiro YAMADA
Hokkaido Math. J. 41(3): 335-364 (October 2012). DOI: 10.14492/hokmj/1351086220

Abstract

Let H be the upper half-space of the Euclidean space. The α-parabolic Bloch type space $¥cal B$α(σ) on H is the set of all solutions u of the parabolic equation (∂/∂t + (−Δx)α)u = 0 with 0 < α ≤ 1 which belong to C1(H) and have finite Bloch norm with weight tσ. In this paper, we study representing and interpolating sequences on parabolic Bloch type spaces. In our previous paper [8], the reproducing formula on $¥cal B$α(σ) is given. A representing sequence gives a discrete version of the reproducing formula on $¥cal B$α(σ). Interpolating sequences are closely related to representing sequences, and such sequences are very interesting in their own right.

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Yôsuke HISHIKAWA. Masahiro YAMADA. "Representing and interpolating sequences on parabolic Bloch type spaces." Hokkaido Math. J. 41 (3) 335 - 364, October 2012. https://doi.org/10.14492/hokmj/1351086220

Information

Published: October 2012
First available in Project Euclid: 24 October 2012

zbMATH: 1252.35011
MathSciNet: MR3012455
Digital Object Identifier: 10.14492/hokmj/1351086220

Subjects:
Primary: 35K05
Secondary: 31B10, 32A18

Rights: Copyright © 2012 Hokkaido University, Department of Mathematics

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Vol.41 • No. 3 • October 2012
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