Fractional powers of closed operators
Fredholm-Stieltjes integral equations with linear constraints: duality theory and Green's function
Fundamental Solutions and Eigenfunction Expansions for Schrödinger Operators . I. Fundamental Solutions.
Integral equations and time varying linear systems.
In this paper we study the resolution problem of an integral equation with operator valued kernel. We prove the equivalence between this equation and certain time varying linear operator system. Sufficient conditions for solving the problem and explicit expressions of the solutions are given.
Integral equations, Volterra equations, and the remarkable resolvent: contractions.
Integral operators and absolute convergence systems.
Integral operators generated by Mercer-like kernels on topological spaces
We analyze some aspects of Mercer's theory when the integral operators act on L²(X,σ), where X is a first countable topological space and σ is a non-degenerate measure. We obtain results akin to the well-known Mercer's theorem and, under a positive definiteness assumption on the generating kernel of the operator, we also deduce series representations for the kernel, traceability of the operator and an integration formula to compute the trace. In this way, we upgrade considerably similar results...
Integral representations of unbounded operators by infinitely smooth kernels
In this paper, we prove that every unbounded linear operator satisfying the Korotkov-Weidmann characterization is unitarily equivalent to an integral operator in L 2(R), with a bounded and infinitely smooth Carleman kernel. The established unitary equivalence is implemented by explicitly definable unitary operators.
-integrability (1 ≤ p ≤ ∞) of a class of integral transforms
Limiting case of the boundedness of fractional integral operators on nonhomogeneous space.
Liouville's operator for a disc in space.
Localization of Singular Integral Operators.
Lp decay estimates for weighted oscillatory integral operators on R.
In this paper, we formulate necessary conditions for decay rates of Lp operator norms of weighted oscillatory integral operators R and give sharp L2 estimates and nearly sharp Lp estimates.
Multi-valued superpositions [Book]
Nonlinear Hammerstein equations and fixed points.
Numerical Bounds for Inverses of Linear Operators
Numerical treatment of fixed point applied to the nonlinear Fredholm integral equation.
On a Class of Fractional Type Integral Equations in Variable Exponent Spaces
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.
On a theorem of Stinespring concerning integral operators of trace class.