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 › peer-review

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

Access to Document

10.3934/dcdss.2018027

Fingerprint Dive into the research topics of 'Some remarks on boundary operators of bessel extensions'. Together they form a unique fingerprint.

Cite this

@article{93f542b780004cceb5ead0905ec6b508,

title = "Some remarks on boundary operators of bessel extensions",

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.",

keywords = "Bessel functions, Boundary operator, Functional calculus, Laplacian, Littlewood-Paley extension",

author = "Jesse Goodman and Spector, {Daniel Eli}",

year = "2018",

month = jun,

day = "1",

doi = "10.3934/dcdss.2018027",

language = "English",

volume = "11",

pages = "493--509",

journal = "Discrete and Continuous Dynamical Systems - Series S",

issn = "1937-1632",

publisher = "American Institute of Mathematical Sciences",

number = "3",

}

TY - JOUR

T1 - Some remarks on boundary operators of bessel extensions

AU - Goodman, Jesse

AU - Spector, Daniel Eli

PY - 2018/6/1

Y1 - 2018/6/1

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

UR - http://www.scopus.com/inward/record.url?scp=85032445179&partnerID=8YFLogxK

U2 - 10.3934/dcdss.2018027

DO - 10.3934/dcdss.2018027

M3 - Article

AN - SCOPUS:85032445179

VL - 11

SP - 493

EP - 509

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

SN - 1937-1632

IS - 3

ER -