Two versions of pseudo-differential operators involving the Kontorovich-Lebedev transform in L2(R+;dx/x)

被引：19
|
作者：
Prasad, Akhilesh [1 ]
Mandal, Upain K. [1 ]
机构：
[1] Indian Sch Mines, Indian Inst Technol, Dept Appl Math, Dhanbad 826004, Bihar, India
来源：
FORUM MATHEMATICUM | 2018年 / 30卷 / 01期
关键词：
Pseudo-differential operator; Kontorovich-Lebedev transform; Hilbert space; PSEUDO-DIFFERENTIAL OPERATORS; CONVOLUTION;
D O I：
10.1515/forum-2016-0254
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Pseudo-differential operators (p.d.o.) L(x, A(x)) and L (x, A(x)) involving the Kontorovich-Lebedev transform are defined. An estimate for these operators in the Hilbert space L-2 (R+; dx/x) is obtained. A symbol class Lambda is defined and it is shown that the product of any two symbols from this class is again in Lambda. At the end, commutators for the p.d.o. and their boundedness results are discussed.
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页码：31 / 42
页数：12
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