Solvability of some integral equations in Hilbert spaces.
Some Estimates of the Remainder in the Expressions for the Eigenvalue Asymptotics of Some Singular Integral Operators
Some global results for nonlinear Sturm-Liouville problems with spectral parameter in the boundary condition
We consider nonlinear Sturm-Liouville problems with spectral parameter in the boundary condition. We investigate the structure of the set of bifurcation points, and study the behavior of two families of continua of nontrivial solutions of this problem contained in the classes of functions having oscillation properties of the eigenfunctions of the corresponding linear problem, and bifurcating from the points and intervals of the line of trivial solutions.
Spectra of partial integral operators with a kernel of three variables
Let Ω= [a, b] × [c, d] and T 1, T 2 be partial integral operators in (Ω): (T 1 f)(x, y) = k 1(x, s, y)f(s, y)ds, (T 2 f)(x, y) = k 2(x, ts, y)f(t, y)dt where k 1 and k 2 are continuous functions on [a, b] × Ω and Ω × [c, d], respectively. In this paper, concepts of determinants and minors of operators E−τT 1, τ ∈ ℂ and E−τT 2, τ ∈ ℂ are introduced as continuous functions on [a, b] and [c, d], respectively. Here E is the identical operator in C(Ω). In addition, Theorems on the spectra of bounded...
Spectral Properties and Asypmtotic Behavior of the Linear Transport Equation.
Spectral Properties of the Cauchy Operator and the Operator of Logarithmic Potential Type on L2 Space With Radial Weight
Spectral Radius Properties for Layer Potentials Associated with the Elsastostatics and Hydrostatics Equations in Nonsmooth Domains.
Spectre du noyau intégral
On construit les fonctions propres sur et les valeurs caractéristiques du noyau de Hilbert-Schmidt . Le spectre est donné par la solution d’une équation transcendante dont le comportement asymptotique est .
The generalized Neumann-Poincaré operator and its spectrum [Book]
The integral equation methods for the perturbed Helmholtz eigenvalue problems.
The smallest positive eigenvalue of a quasisymmetric automorphism of the unit circle
This paper provides sufficient conditions on a quasisymmetric automorphism γ of the unit circle which guarantee the existence of the smallest positive eigenvalue of γ. They are expressed by means of a regular quasiconformal Teichmüller self-mapping φ of the unit disc Δ. In particular, the norm of the generalized harmonic conjugation operator is determined by the maximal dilatation of φ. A characterization of all eigenvalues of a quasisymmetric automorphism γ in terms of the smallest positive eigenvalue...
The spectrum of the transport operator with a potential term under the spatial periodicity condition
Variational theory of set-valued Hammerstein operators in Banach function spaces. The eigenvalue problem
Wiener-Hopf integral operators with PC symbols on spaces with Muckenhoupt weight.
We describe the spectrum and the essential spectrum and give an index formula for Wiener-Hopf integral operators with piecewise continuous symbols on the space Lp(R+,ω) with a Muckenhoupt weight ω. Our main result says that the essential spectrum is a set resulting from the essential range of the symbol by joining the two endpoints of each jump by a certain sickle-shaped domain, whose shape is completely determined by the value of p and the behavior of the weight ω at the origin and at infinity.
Асимптотическое поведение спектра интегральных операторов с особенностью на диагонали
О новых неравенствах для характеристических чисел интегральных уравнений с гладкими ядрами
О системах интегральных уравнений
О скорости убывания собственных чисел оператора Фредгольма.
О собственных функциях одного интегрального уравнения
Об устойчивости собственных значений сингулярных интегральных уравнений