Related papers: A remark on analytic Fredholm alternative

Using the relation established by Johnson--Zumbrun between Hill's method of aproximating spectra of periodic-coefficient ordinary differential operators and a generalized periodic Evans function given by the $2$-modified characteristic…

We study the existence of solutions to abstract equations of the form $0 = Au + F(u)$, $u\in K\subset E$, where A is an abstract differential operator acting in a Banach space $E$, $K$ is a closed convex set of constraints being invariant…

This paper concerns Fredholm theory in several variables, and its applications to Hilbert spaces of analytic functions. One feature is the introduction of ideas from commutative algebra to operator theory. Specifically, we introduce a…

We give a semiclassical analysis of a nonlinear eigenvalue problem arising from the study of the failure of analytic hypoellipticity and obtain a general family of hypoelliptic, but not analytic hypoelliptic operators.

In this paper we construct a weakly-nonlinear d'Alembert-type solution of the Cauchy problem for a Boussinesq-Klein-Gordon equation. Similarly to our earlier work based on the use of spatial Fourier series, we consider the problem in the…

Using the method of Rudin-Shapiro polynomials we prove the analytic version of the Mitiagin-DeLeeuw-Mirkhil non-inequality for complex partial differential operators with constant coefficients on bi-disc.

The Fredholm integral equations of the first kind are a classical example of ill-posed problem in the sense of Hadamard. If the integral operator is self-adjoint and admits a set of eigenfunctions, then a formal solution can be written in…

By applying new functional analysis tools in the framework of Fourier interpolation formulas, such as sc-Fredholm operators and Schauder frames, we are able to improve and refine several properties of these aforementioned formulas on the…

We establish a Fredholm criterion for an arbitrary operator in the Banach algebra of singular integral operators with piecewise continuous coefficients on Nakano spaces (generalized Lebesgue spaces with variable exponent) with Khvedelidze…

The Boutet de Monvel calculus of pseudo-differential boundary operators is generalised to the full scales of Besov and Triebel--Lizorkin spaces (though with finite integral exponents for the latter). The continuity and Fredholm properties…

We put together the ingredients for an efficient operator calculus based on Krawtchouk polynomials, including Krawtchouk transforms and corresponding convolution structure which provide an inherently discrete alternative to Fourier…

Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are…

Subharmonic functions associated with the stationary Schrodinger operator are its weak subsolutions under appropriate assumptions on the potential of the operator. We prove for these functions analogs of several classical results on…

This paper is in concern with Cauchy problems involving the fractional derivatives with respect to another function. Results of existence, uniqueness, and Taylor series among others are established in appropriate functional spaces. We prove…

We introduce and study weighted spaces of functions with mixed norm on the upper half-plane, defined in terms of Fourier transform. We give a characterization of analytic functions within these spaces, and in particular, we provide an…

We prove a Fredholm determinantal identity for the tilted Toeplitz minor $$ D_{N}^{\xi,\theta}(\varphi):= \det\bigl[(\theta_{i}\xi_{j}\varphi)_{i-j}\bigr]_{i,j=1}^{N}, $$ generalizing the Borodin-Okounkov-Geronimo-Case (BOGC) identity to…

We construct a new bounded functional calculus for the generators of bounded semigroups on Hilbert spaces and generators of bounded holomorphic semigroups on Banach spaces. The calculus is a natural (and strict) extension of the classical…

The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be effectively studied in that level of…

We derive analytic solutions for the full time dependence of space-fractional Fokker-Planck equations corresponding to stochastic Langevin equations with additive tempered-stable L\'{e}vy noise terms. The drift terms are generalised to be…

Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function defining the space. Inside the spectrum of the inner function, Ahern and Clark showed that under some…