Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Two versions of pseudo-differential operators involving the Kontorovich–Lebedev transform in L 2(ℝ+;dx/x)

Two versions of pseudo-differential operators involving the Kontorovich–Lebedev transform in L... AbstractThe Pseudo-differential operators (p.d.o.) L⁢(x,Ax){L(x,A_{x})}and ℒ⁢(x,Ax){\mathcal{L}(x,A_{x})}involving the Kontorovich–Lebedev transform are defined. An estimate for these operators in the Hilbert space L2⁢(ℝ+;d⁢xx){L^{2}(\mathbb{R}_{+};\frac{dx}{x})}is obtained. A symbol class Λ is defined and it is shown that the product of any two symbols from this class is again in Λ. At the end, commutators for the p.d.o. and their boundedness results are discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Two versions of pseudo-differential operators involving the Kontorovich–Lebedev transform in L 2(ℝ+;dx/x)

Prasad, Akhilesh; Mandal, Upain K.
Forum Mathematicum , Volume 30 (1): 12 – Jan 1, 2018
Download PDF
12 pages

Loading next page...
 
/lp/de-gruyter/two-versions-of-pseudo-differential-operators-involving-the-qcJJahPUH0

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
© 2019 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2016-0254
Publisher site
See Article on Publisher Site

Abstract

AbstractThe Pseudo-differential operators (p.d.o.) L⁢(x,Ax){L(x,A_{x})}and ℒ⁢(x,Ax){\mathcal{L}(x,A_{x})}involving the Kontorovich–Lebedev transform are defined. An estimate for these operators in the Hilbert space L2⁢(ℝ+;d⁢xx){L^{2}(\mathbb{R}_{+};\frac{dx}{x})}is obtained. A symbol class Λ is defined and it is shown that the product of any two symbols from this class is again in Λ. At the end, commutators for the p.d.o. and their boundedness results are discussed.

Journal

Forum Mathematicum – de Gruyter

Published: Jan 1, 2018

There are no references for this article.