Some existence and uniqueness theorems are established for weakly singular Volterra and Fredholm-Volterra integral equations in C[a, b]. Our method is based on fixed point theorems which are applied to the iterated operator and we apply the fiber Picard operator theorem to establish differentiability with respect to parameter. This method can be applied only for linear equations because otherwi...

In the monograph [2], the authors define the operator spectrum σ op (A) of a band-dominated operator A (these terms are defined below) and prove that A is Fredholm if and only if all of the operators in σ op (A) are invertible with uniformly bounded inverses. They also ask whether the uniform boundedness condition can in fact be dispensed with. In this note we answer this question affirmatively.

I show that the dynamical determinant, associated to an Anosov diffeomorphism, is the Fredholm determinant of the corresponding RuellePerron-Frobenius transfer operator acting on appropriate Banach spaces. As a consequence it follows, for example, that the zeroes of the dynamical determinant describe the eigenvalues of the transfer operator and the Ruelle resonances and that, for C∞ Anosov diff...

We study the strongly singular volume integral operator that describes the scattering of time-harmonic electromagnetic waves. For the case of piecewise constant material coefficients and smooth interfaces, we determine the essential spectrum. We show that it is a finite set and that the operator is Fredholm of index zero in H(curl) if and only if the relative permeability and permittivity are b...

Abstract We define and study Toeplitz operators on the Fréchet space of all holomorphic functions finitely connected domains in Riemann sphere. completely characterize Fredholm, semi-Fredholm invertible belonging to this class. As a result, we obtain characterization these classes unit disk case. motivation formulate analyze Riemann–Hilbert problem which consider.

In this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. By using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. Also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Moreover, we investigate the ...

In this paper we analyze a discrete time single server queue where the service time equals one slot The numbers of arrivals in each slot are assumed to be independent and identically distributed random variables The service process is interrupted by a semi Markov process namely in certain states the server is available for service while the server is not available in other states We analyze bot...