scholarly journals Metrics on test function spaces for canonical field operators

1970 ◽  
Vol 16 (4) ◽  
pp. 329-346 ◽  
Author(s):  
Gerhard C. Hegerfeldt ◽  
John R. Klauder
Keyword(s):  
Function Spaces ◽  
Test Function

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

scholarly journals The composition of linear canonical wavelet transforms on generalized function spaces

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 4123-4136
Author(s):  
Akhilesh Prasad ◽  
Z.A. Ansari
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Function Spaces ◽  
Generalized Function ◽  
Test Function ◽  
Boundedness Result

The main goal of this paper is to study the continuity of composition of linear canonical wavelet transform (LCWTs) on generalized test function spaces Lp,A, Gp,A and BA(R3). The boundedness result for composition of linear canonical wavelet transforms on Hps,A is given.

scholarly journals A Convenient Notion of Compact Set for Generalized Functions

2017 ◽  
Vol 61 (1) ◽  
pp. 57-92
Author(s):  
Paolo Giordano ◽  
Michael Kunzinger
Keyword(s):  
Function Spaces ◽  
Generalized Functions ◽  
Distribution Theory ◽  
Compact Set ◽  
Compact Sets ◽  
Smooth Functions ◽  
Test Function ◽  
Compactly Supported ◽  
Nonlinear Generalized Functions

We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to transfer, as far as possible, properties enjoyed by standard smooth functions on compact sets into the framework of generalized functions. Based on this concept, we introduce spaces of compactly supported generalized smooth functions that are close analogues to the test function spaces of distribution theory. We then develop the topological and functional–analytic foundations of these spaces.

Sign in / Sign up

Export Citation Format

Share Document