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 language | English |
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Pages (from-to) | 493-509 |
Number of pages | 17 |
Journal | Discrete and Continuous Dynamical Systems - Series S |
Volume | 11 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jun 2018 |
Keywords
- Bessel functions
- Boundary operator
- Functional calculus
- Laplacian
- Littlewood-Paley extension