We propose and investigate a method for the stable determination of a harmonic function from knowledge of its value and its normal derivative on a part of the boundary of the (bounded) solution domain (Cauchy problem). We reformulate the Cauchy problem as an operator equation on the boundary using the Dirichlet-to-Neumann map. To discretize the obtained operator, we modify and employ a method d...

We consider real-analytic maps of the interval I = [0, 1] which are expanding everywhere except for a neutral fixed point at 0. We show that on a certain function space the spectrum of the associated Perron-Frobenius operator M has a decomposition sp(M) = σc ∪ σp where σc = [0, 1] is the continuous spectrum of M and σp is the pure point spectrum with no points of accumulation outside 0 and 1. W...

In this paper we are concerned with the spectral analysis for classes of finte rank perturbations diagonal operators in form A = D+F where D is a operator and F u’1 ⊗v’1+...+u’m ⊗vm an finite non-archimedean Banach space countable type. We compute spectrum using theory Fredholm non archimedean setting concept essential linear operators.

Abstract The aim of this paper is to provide necessary and sufficient conditions on the generator a multiplication operator acting in spaces functions bounded Young Riesz variation so that it is, among other things, invertible, continuous, finite rank, compact, Fredholm or has closed range. Furthermore, we characterize various spectra such operators give some estimates their measure non-compact...

The article deals with the existence of solutions an integro-differential equation in case anomalous diffusion negative Laplace operator a fractional power presence transport term. proof is based on fixed point technique. Solvability conditions for elliptic operators without Fredholm property unbounded domains are used. We discuss how introduction term impacts regularity solutions.

In [24], Koliha proved that T ? L(X) (X is a complex Banach space) generalized Drazin invertible operator iff there exists an S commuting with such STS = and ?(T2S?T) {0} 0 < acc ?(T). Later, in [14, 34] the authors extended class of operators they also pseudo-Fredholm introduced by Mbekhta [27] other classes semi-Fredholm operators. As continuation these works, we introduce study 1zinvertib...

The linearized collision operator of the Boltzmann equation can in a natural way be written as sum positive multiplication operator, frequency, and an integral operator. Compactness for monatomic single species is classical result, while corresponding results mixtures polyatomic where polyatomicity modeled by discrete internal energy variable, are more recently obtained. In this work compactnes...

The index of a selfadjoint Fredholm operator is zero by the well-known fact that kernel perpendicular to its range. was generalised families Atiyah and Jänich in sixties, it readily seen that, on complex Hilbert spaces, this so-called bundle vanishes for operators as case single operator. first aim note point out every real space compact topological $X$, there family parametrised $X\times S^1$ ...