Abstract The paper suggests a new technique for solution of the inverse problem for Maxwell’s equations in a dissipating medium. Being non-self-adjoint, the problem generally requires computing an adjoint operator on each step of gradient descent minimization procedure. The suggested approach introduces a conjugation operator and develops a representation of the system of Maxwell’s equations ba...

In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form Lu := −[pu∇]∆ + qu, on an arbitrary, bounded time-scale T, for suitable functions p, q, together with suitable boundary conditions. We show that, with a suitable choice of domain, this operator can be formulated in the Hilbert space L(Tκ), in such a way that the resulting operator is self-adjoint,...

We perform a semi-classical study of chiral symmetry breaking and of the spectrum of the Dirac operator in QCD with adjoint fermions. For this purpose we calculate matrix elements of the adjoint Dirac operator between instanton zero modes and study their symmetry properties. We present simulations of the instanton ensemble for different numbers of Majorana fermions in the adjoint representation...

We provide the mathematical foundation for the Xm-Jacobi spectral theory. Namely, we present a self-adjoint operator associated to the differential expression with the exceptional Xm-Jacobi orthogonal polynomials as eigenfunctions. This proves that those polynomials are indeed eigenfunctions of the self-adjoint operator (rather than just formal eigenfunctions). Further, we prove the completenes...

We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form (1− 〈z, w〉)−γ for γ > 0. We find necessary and sufficient conditions for the adjoint of a weighted composition operator to be a weighted composition operator or the inverse of a weighted composition operator. We then obtain characterizations of self-adjoint and unitary weigh...

In this paper we consider the problem of the existence of higher derivatives of the function t → ϕ(A + tK), where ϕ is a function on the real line, A is a self-adjoint operator, and K is a bounded self-adjoint operator. We improve earlier results by Sten'kin. In order to do this, we give a new approach to multiple operator integrals. This approach improves the earlier approach given by Sten'kin...

The recently introduced concept of a spectral shift operator is applied in several instances. Explicit applications include Krein's trace formula for pairs of self-adjoint operators, the Birman-Solomyak spectral averaging formula and its operator-valued extension, and an abstract approach to trace formulas based on perturbation theory and the theory of self-adjoint extensions of symmetric opera...