Hokkaido Mathematical Journal

Representing and interpolating sequences on parabolic Bloch type spaces

Yôsuke HISHIKAWA and Masahiro YAMADA

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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.

Article information

Hokkaido Math. J., Volume 41, Number 3 (2012), 335-364.

First available in Project Euclid: 24 October 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K05: Heat equation
Secondary: 31B10: Integral representations, integral operators, integral equations methods 32A18: Bloch functions, normal functions

Bloch space parabolic operator of fractional order representing sequence interpolating sequence


HISHIKAWA, Yôsuke; YAMADA, Masahiro. Representing and interpolating sequences on parabolic Bloch type spaces. Hokkaido Math. J. 41 (2012), no. 3, 335--364. doi:10.14492/hokmj/1351086220. https://projecteuclid.org/euclid.hokmj/1351086220

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