Integral Operators in Potential Theory

1980 ◽  
Author(s):  
Josef Král
Keyword(s):  
Potential Theory ◽  
Integral Operators

On the spectra of some integral operators related to the potential theory in the plane

2010 ◽  
Vol 33 (14) ◽  
pp. 1685-1691 ◽  
Author(s):  
Oleg F. Gerus ◽  
Vladimir N. Kutrunov ◽  
Michael Shapiro
Keyword(s):  
Potential Theory ◽  
Integral Operators

scholarly journals Some spectral properties of an integral operator in potential theory

1986 ◽  
Vol 29 (3) ◽  
pp. 405-411 ◽  
Author(s):  
John F. Ahner
Keyword(s):  
Potential Theory ◽  
Spectral Properties ◽  
Three Dimensional ◽  
Single Layer ◽  
Integral Operators ◽  
Normal Derivative ◽  
Potential Operator ◽  
Single Layer Potential ◽  
Layer Potential ◽  
Integral Equation Methods

In [7] Plemelj established some fundamental results in two- and three-dimensional potential theory about the eigenvalues of both the double layer potential operator and its adjoint, the normal derivative of the single layer potential operator. In [3] Blumenfeld and Mayer established some additional results concerning the eigenvalues of these integral operators in the case of ℝ2. The spectral properties established by Plemelj [7] and by Blumenfeld and Mayer [3] have had a profound effect in the area of integral equation methods in scattering and potential theory in both ℝ2 and ℝ3.

Spectral Properties of Some Integral Operators Arising in Potential Theory

1992 ◽  
Vol 43 (4) ◽  
pp. 387-407 ◽  
Author(s):  
J. M. Anderson ◽  
D. Khavinson ◽  
V. Lomonosov
Keyword(s):  
Potential Theory ◽  
Spectral Properties ◽  
Integral Operators

On the Fredholm radius of integral operators of potential theory

1993 ◽  
Vol 64 (6) ◽  
pp. 1297-1313 ◽  
Author(s):  
N. V. Grachev ◽  
V. G. Maz'ya
Keyword(s):  
Potential Theory ◽  
Integral Operators ◽  
Fredholm Radius

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.

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