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On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

Rafeiro, Humberto, Samko, Stefan (2007)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30We obtain a criterion of Fredholmness and formula for the Fredholm index of a certain class of one-dimensional integral operators M with a weak singularity in the kernel, from the variable exponent Lebesgue space L^p(·) ([a, b], ?) to the Sobolev type space L^α,p(·) ([a, b], ?) of fractional smoothness. We also give formulas of closed form solutions ϕ ∈ L^p(·) of the 1st kind integral equation M0ϕ = f, known as the generalized...

On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball.

Stević, Stevo (2008)

Discrete Dynamics in Nature and Society

On a theorem of Stinespring concerning integral operators of trace class.

R.A. Lorentz, W.P. Kamp, P.A. Rejto (1989)

Journal für die reine und angewandte Mathematik

On integral operators with operator-valued kernels.

Shahmurov, Rishad (2010)

Journal of Inequalities and Applications [electronic only]

On K-transform.

Nasim, C. (1981)

International Journal of Mathematics and Mathematical Sciences

On solvability of nonlinear equations.

Lavrent'ev, I.M., Sćepanović, R. (1984)

Publications de l'Institut Mathématique. Nouvelle Série

On some structural properties of Banach function spaces and boundedness of certain integral operators

T. S. Kopaliani (2004)

Czechoslovak Mathematical Journal

In this paper the notions of uniformly upper and uniformly lower $ℓ$ -estimates for Banach function spaces are introduced. Further, the pair $(X, Y)$ of Banach function spaces is characterized, where $X$ and $Y$ satisfy uniformly a lower $ℓ$ -estimate and uniformly an upper $ℓ$ -estimate, respectively. The integral operator from $X$ into $Y$ of the form $K f (x) = ϕ (x) \int_{0}^{x} k (x, y) f (y) ψ (y) d y$ is studied, where $k$ , $ϕ$ , $ψ$ are prescribed functions under some local integrability conditions, the kernel $k$ is non-negative and is assumed to satisfy certain additional...

On the integral operators of the third kind.

Korotkov, V.B. (2003)

Sibirskij Matematicheskij Zhurnal

On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator

S. M. Bahri (2012)

Mathematica Bohemica

In the present work, using a formula describing all scalar spectral functions of a Carleman operator $A$ of defect indices $(1, 1)$ in the Hilbert space $L^{2} (X, μ)$ that we obtained in a previous paper, we derive certain results concerning the localization of the spectrum of quasi-selfadjoint extensions of the operator $A$ .

On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree $- n$ .

Avsyankin, O. G., Karapetyants, N. K. (2003)

Sibirskij Matematicheskij Zhurnal

On the solution of the Liouville equation over a rectangle.

Arthurs, A.M., Clegg, J., Nagar, A.K. (1996)

Journal of Applied Mathematics and Stochastic Analysis

On the Spectra of Finite-Dimensional Pertobations of Matrix Multiplication Operators.

I. Gohberg, E. Azoff, K. Clancey (1979/1980)

Manuscripta mathematica

On the two-fold symbol chain of a C*-algebra of singular integral operators on a polycylinder.

Heinz O. Cordes (1986)

Revista Matemática Iberoamericana

On weighted Hadamard-type singular integrals and their applications.

Xu, Yong Jia (2007)

Abstract and Applied Analysis

Opérateurs intégro-différentiels méromorphes et opérateurs aux différences

Anne Duval (1987)

Annales de l'institut Fourier

On introduit une classe d’opérateurs intégro-différentiels d’ordre infini, à coefficients méromorphes et pour lesquels les séries majorantes sont de type Dirichlet. On établit des résultats algébriques : caractérisation des éléments inversibles, théorèmes de division et de préparation. En les faisant opérer sur divers espaces de séries et de fonctions on obtient des théorèmes d’indices et des résultats de surjectivité. Après transformation de Mellin ces opérateurs permettent d’étudier les “solutions”...

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