Some remarks on boundary operators of bessel extensions

Jesse Goodman, Daniel Eli Spector*

*Corresponding author for this work

Research output: Contribution to journalArticle

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 - 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.

Original languageEnglish
Pages (from-to)493-509
Number of pages17
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume11
Issue number3
DOIs
StatePublished - 1 Jun 2018

Keywords

  • Bessel functions
  • Boundary operator
  • Functional calculus
  • Laplacian
  • Littlewood-Paley extension

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