Eigenvalue Distribution of Integral Operators

1986 ◽  
pp. 143-216
Author(s):  
Hermann König
Keyword(s):  
Integral Operators ◽  
Eigenvalue Distribution

scholarly journals Interpolation methods to estimate eigenvalue distribution of some integral operators

2004 ◽  
Vol 2004 (9) ◽  
pp. 479-485
Author(s):  
E. M. El-Shobaky ◽  
N. Abdel-Mottaleb ◽  
A. Fathi ◽  
M. Faragallah
Keyword(s):  
Besov Space ◽  
Asymptotic Distribution ◽  
Function Space ◽  
Integral Operators ◽  
Eigenvalue Distribution ◽  
Factorization Theorem ◽  
Lizorkin Space ◽  
Interpolation Methods ◽  
Distribution Of Eigenvalues

We study the asymptotic distribution of eigenvalues of integral operatorsTkdefined by kernelskwhich belong to Triebel-Lizorkin function spaceFpuσ(F  qvτ)by using the factorization theorem and the Weyl numbersxn. We use the relation between Triebel-Lizorkin spaceFpuσ(Ω)and Besov spaceBpqτ(Ω)and the interpolation methods to get an estimation for the distribution of eigenvalues in Lizorkin spacesFpuσ(F  qvτ).

Multianisotropic integral operators defined by regular equations

2018 ◽  
Vol 60 (3) ◽  
pp. 610-629
Author(s):  
G. A. Karapetyan ◽  
H. A. Petrosyan
Keyword(s):  
Integral Operators

Multi-parameter Singular Integrals II: General Theory

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
General Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Main Issue

This chapter turns to a general theory which generalizes and unifies all of the examples in the preceding chapters. A main issue is that the first definition from the trichotomy does not generalize to the multi-parameter situation. To deal with this, strengthened cancellation conditions are introduced. This is done in two different ways, resulting in four total definitions for singular integral operators (the first two use the strengthened cancellation conditions, while the later two are generalizations of the later two parts of the trichotomy). Thus, we obtain four classes of singular integral operators, denoted by A1, A2, A3, and A4. The main theorem of the chapter is A1 = A2 = A3 = A4; i.e., all four of these definitions are equivalent. This leads to many nice properties of these singular integral operators.

The Calder´on-Zygmund Theory I: Ellipticity

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Classical Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Differential Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Partial Differential ◽  
Translation Invariant ◽  
Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

Regularization of Integral Operators in Singularly Perturbed Problems Using Normal Forms

Vestnik MEI ◽  
2019 ◽  
Vol 6 ◽  
pp. 131-137
Author(s):  
Abdukhafiz A. Bobodzhanova ◽  
◽  
Valeriy F. Safonov ◽  
Keyword(s):  
Normal Forms ◽  
Integral Operators ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems
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