TY - JOUR
T1 - Some remarks on boundary operators of bessel extensions
AU - Goodman, Jesse
AU - Spector, Daniel
N1 - Funding Information:
Acknowledgments. The authors would like to thank Cindy Chen for her help in obtaining some of the articles utilized in this research and the Technion for the stimulating environment that led to the initiation of this collaboration. D.S. would like to thank the University of Auckland for its warm hospitality during which some of this research was undertaken. D.S. is supported in part by the Taiwan Ministry of Science and Technology under research grants 103-2115-M-009-016-MY2 and 105-2115-M-009-004-MY2. J.G. would like to thank the National Chiao Tung University for its warm hospitality during which some of this research was undertaken. J.G. is supported in part by the Marsden Fund Council from New Zealand Government funding, managed by the Royal Society of New Zealand.
Funding Information:
2010 Mathematics Subject Classification. Primary: 35J70; Secondary: 47D03, 33C10. Key words and phrases. Boundary operator, Littlewood-Paley extension, Bessel functions, functional calculus, Laplacian. The first author is supported in part by the Marsden Fund Council from New Zealand Government funding, managed by the Royal Society of New Zealand. The second author is supported in part by the Taiwan Ministry of Science and Technology under research grants 103-2115-M-009-016-MY2 and 105-2115-M-009-004-MY2. ∗ Corresponding author: [email protected].
PY - 2018/6
Y1 - 2018/6
N2 - 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.
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.
KW - Bessel functions
KW - Boundary operator
KW - Functional calculus
KW - Laplacian
KW - Littlewood-Paley extension
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U2 - 10.3934/dcdss.2018027
DO - 10.3934/dcdss.2018027
M3 - Article
AN - SCOPUS:85032445179
SN - 1937-1632
VL - 11
SP - 493
EP - 509
JO - Discrete and Continuous Dynamical Systems - Series S
JF - Discrete and Continuous Dynamical Systems - Series S
IS - 3
ER -