Spectral Theory, Function Spaces and Inequalities

2012 ◽  
Keyword(s):  
Spectral Theory ◽  
Function Spaces

scholarly journals Some Applications of the Spectral Theory for the Integral Transform Involving the Spectral Representation

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hyun Soo Chung ◽  
Seung Jun Chang
Keyword(s):  
Quantum Mechanics ◽  
Function Space ◽  
Spectral Theory ◽  
Spectral Representation ◽  
Integral Transform ◽  
Adjoint Operator ◽  
Function Spaces

In many previous papers, an integral transformℱγ,βwas just considered as a transform on appropriate function spaces. In this paper we deal with the integral transform as an operator on a function space. We then apply various operator theories toℱγ,β. Finally we give an application for the spectral representation of a self-adjoint operator which plays a key role in quantum mechanics.

To the spectral theory of partially ordered sets

2018 ◽  
Vol 60 (3) ◽  
pp. 578-598
Author(s):  
Yu. L. Ershov ◽  
M. V. Schwidefsky
Keyword(s):  
Spectral Theory ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

SPECTRAL THEORY OF 2-D PHOTONIC CRYSTALS: ANALYTICAL GROUNDS

2016 ◽  
Vol 75 (16) ◽  
pp. 1417-1433 ◽  
Author(s):  
Yurii Konstantinovich Sirenko ◽  
K. Yu. Sirenko ◽  
H. O. Sliusarenko ◽  
N. P. Yashina
Keyword(s):  
Photonic Crystals ◽  
Spectral Theory

Function Spaces and Nonsymmetric Norm Preserving Maps

2018 ◽  
Vol 25 (5) ◽  
pp. 729-740
Author(s):  
Hadis Pazandeh ◽  
Fereshteh Sady
Keyword(s):  
Function Spaces

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?.

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