Some remarks on boundary operators of bessel extensions

Jesse Goodman; Daniel Eli Spector

doi:10.3934/dcdss.2018027

Some remarks on boundary operators of bessel extensions

Jesse Goodman, Daniel Eli Spector^*

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article

2 Scopus citations

Abstract

In this paper we study some boundary operators of a class of Bessel-type Littlewood-Paley extensions whose prototype is ?xu(x, y) + ^{1 - 2}s^?u_?y (x, y) + ^?_?y^2u₂ (x, y) = 0 for x ? R^d, y > 0, y u(x, 0) = f(x) for x ? R^d. In particular, we show that with a logarithmic scaling one can capture the failure of analyticity of these extensions in the limiting cases s = k ? N.

Original language	English
Pages (from-to)	493-509
Number of pages	17
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	11
Issue number	3
DOIs	https://doi.org/10.3934/dcdss.2018027
State	Published - 1 Jun 2018

Keywords

Bessel functions
Boundary operator
Functional calculus
Laplacian
Littlewood-Paley extension

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10.3934/dcdss.2018027

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Goodman, J., & Spector, D. E. (2018). Some remarks on boundary operators of bessel extensions. Discrete and Continuous Dynamical Systems - Series S, 11(3), 493-509. https://doi.org/10.3934/dcdss.2018027

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AB - In this paper we study some boundary operators of a class of Bessel-type Littlewood-Paley extensions whose prototype is ?xu(x, y) + 1 - 2s?u?y (x, y) + ??y2u2 (x, y) = 0 for x ? Rd, y > 0, y u(x, 0) = f(x) for x ? Rd. In particular, we show that with a logarithmic scaling one can capture the failure of analyticity of these extensions in the limiting cases s = k ? N.

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KW - Laplacian

KW - Littlewood-Paley extension

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