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Papers by Anna Mitina
Journal of Integral Equations and Applications, Dec 1, 2007
We show that the problem can be reduced to one or more problems of the type: (2) ψ(x) = T ψ(x) + ... more We show that the problem can be reduced to one or more problems of the type: (2) ψ(x) = T ψ(x) + φ(x) with a compact operator T and a vector function φ(x) such that e sx φ(x) ∈ L(0, ∞). The unknown function ψ(x) satisfies the same condition: e sx ψ(x) ∈ L(0, ∞). The compactness of T allows us to apply Riesz-Banach theory of linear equations with such operators and establish a Fredholm alternative for (1) and (2). We will also find some additional conditions under which T is a contraction, so that equation (2) has one and only one solution which can be found by an iteration.
Journal of Integral Equations and Applications, Dec 1, 1994
The asymptotic behavior of the solutions of a class of integro-differential equations on positive... more The asymptotic behavior of the solutions of a class of integro-differential equations on positive half-axis with non-difference kernel is investigated. The solutions are equal asymptotically to the sum of terms having the form of product of an exponent e p k x and a polynomial. Numbers p k are zeros of a function which is found in explicit form. Location of these zeros in the complex plane is also investigated. To obtain these results the technique of analytical continuation is used.
Physics Reports, Sep 1, 1997
In the present review the development of the theory of the anomalous skin effect in normal metals... more In the present review the development of the theory of the anomalous skin effect in normal metals is discussed. The dependence of the impedance on the mean free path of the conduction electrons becomes anomalous for certain directions of electromagnetic wave propagation if there are singular points (points of parabolic type, points with zero curvature) on the Fermi surface. The influence of the gain part of the collision integral on the impedance is analyzed in detail when the metal is isotropic. It is shown how the gain term affects the value of the surface conductivity under the diffuse reflection of electrons from the metal surface.
Journal of Integral Equations and Applications, Dec 1, 1995
Journal of Integral Equations and Applications, Dec 1, 2001
In what follows we assume that the parameter ν is large enough unless the opposite is stated.
Low Temperature Physics, 1997
An algorithm for calculating the surface impedance of a normal isotropic metal is constructed by ... more An algorithm for calculating the surface impedance of a normal isotropic metal is constructed by taking into account the arriving term in the collision integral ͑in the case of specular reflection͒. Analytic expressions are obtained for scattering probability describing the s-, p-, and d-scattering.
Journal of Integral Equations and Applications, 1995
Journal of Integral Equations and Applications, 2007
We show that the problem can be reduced to one or more problems of the type: (2) ψ(x) = T ψ(x) + ... more We show that the problem can be reduced to one or more problems of the type: (2) ψ(x) = T ψ(x) + φ(x) with a compact operator T and a vector function φ(x) such that e sx φ(x) ∈ L(0, ∞). The unknown function ψ(x) satisfies the same condition: e sx ψ(x) ∈ L(0, ∞). The compactness of T allows us to apply Riesz-Banach theory of linear equations with such operators and establish a Fredholm alternative for (1) and (2). We will also find some additional conditions under which T is a contraction, so that equation (2) has one and only one solution which can be found by an iteration.
Journal of Integral Equations and Applications, 2001
In what follows we assume that the parameter ν is large enough unless the opposite is stated.
Journal of Integral Equations and Applications, Dec 1, 2007
We show that the problem can be reduced to one or more problems of the type: (2) ψ(x) = T ψ(x) + ... more We show that the problem can be reduced to one or more problems of the type: (2) ψ(x) = T ψ(x) + φ(x) with a compact operator T and a vector function φ(x) such that e sx φ(x) ∈ L(0, ∞). The unknown function ψ(x) satisfies the same condition: e sx ψ(x) ∈ L(0, ∞). The compactness of T allows us to apply Riesz-Banach theory of linear equations with such operators and establish a Fredholm alternative for (1) and (2). We will also find some additional conditions under which T is a contraction, so that equation (2) has one and only one solution which can be found by an iteration.
Journal of Integral Equations and Applications, Dec 1, 1994
The asymptotic behavior of the solutions of a class of integro-differential equations on positive... more The asymptotic behavior of the solutions of a class of integro-differential equations on positive half-axis with non-difference kernel is investigated. The solutions are equal asymptotically to the sum of terms having the form of product of an exponent e p k x and a polynomial. Numbers p k are zeros of a function which is found in explicit form. Location of these zeros in the complex plane is also investigated. To obtain these results the technique of analytical continuation is used.
Physics Reports, Sep 1, 1997
In the present review the development of the theory of the anomalous skin effect in normal metals... more In the present review the development of the theory of the anomalous skin effect in normal metals is discussed. The dependence of the impedance on the mean free path of the conduction electrons becomes anomalous for certain directions of electromagnetic wave propagation if there are singular points (points of parabolic type, points with zero curvature) on the Fermi surface. The influence of the gain part of the collision integral on the impedance is analyzed in detail when the metal is isotropic. It is shown how the gain term affects the value of the surface conductivity under the diffuse reflection of electrons from the metal surface.
Journal of Integral Equations and Applications, Dec 1, 1995
Journal of Integral Equations and Applications, Dec 1, 2001
In what follows we assume that the parameter ν is large enough unless the opposite is stated.
Low Temperature Physics, 1997
An algorithm for calculating the surface impedance of a normal isotropic metal is constructed by ... more An algorithm for calculating the surface impedance of a normal isotropic metal is constructed by taking into account the arriving term in the collision integral ͑in the case of specular reflection͒. Analytic expressions are obtained for scattering probability describing the s-, p-, and d-scattering.
Journal of Integral Equations and Applications, 1995
Journal of Integral Equations and Applications, 2007
We show that the problem can be reduced to one or more problems of the type: (2) ψ(x) = T ψ(x) + ... more We show that the problem can be reduced to one or more problems of the type: (2) ψ(x) = T ψ(x) + φ(x) with a compact operator T and a vector function φ(x) such that e sx φ(x) ∈ L(0, ∞). The unknown function ψ(x) satisfies the same condition: e sx ψ(x) ∈ L(0, ∞). The compactness of T allows us to apply Riesz-Banach theory of linear equations with such operators and establish a Fredholm alternative for (1) and (2). We will also find some additional conditions under which T is a contraction, so that equation (2) has one and only one solution which can be found by an iteration.
Journal of Integral Equations and Applications, 2001
In what follows we assume that the parameter ν is large enough unless the opposite is stated.