Related papers: Fredholm Differential Operators with Unbounded Coe…

This paper ascertains the global behavior of the forward and backward branches of solutions provided by the Leray-Schauder continuation theorem for orientable $\mathcal{C}^1$ Fredholm maps, as developed by the authors in [54]. Under…

We investigate the linear telegraph equation $$ u_{tt}-u_{xx}+2\mu u_t=f(x,t) $$ with periodic Neumann boundary conditions. We prove that the operator of the problem is modeled as a Fredholm operator of index zero in the scale of…

This paper has aim to characterize Fredholmness and Weylness of upper triangular operator matrices having arbitrary dimension n. We present various characterization results in the setting of infinite dimensional Hilbert spaces, thus…

In this paper we consider A-Fredholm and semi-A-Fredholm operators on Hilbert C*-modules over a W*-algebra A defined in [3],[10]. Using the assumption that A is a W*-algebra (and not an arbitrary C*-algebra), we obtain several results such…

We completely characterize smoothness of bounded linear operators between infinite dimensional real normed linear spaces, probably for the very first time, by applying the concepts of Birkhoff-James orthogonality and semi-inner-products in…

We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family $\GR \to B$ of Lie groups (these families are called ``gauge-invariant families'' in what follows). If the fibers…

An algebraic analogue of the family of Fredholm operators is introduced for the family of row and column finite matrices, dubbed "Fredholm matrices." In addition, a measure is introduced which indicates how far a Fredholm matrix is from an…

We investigate elliptic boundary-value problems for which the maximum of the orders of the boundary operators is equal to or greater than the order of the elliptic differential equation. We prove that the operator corresponding to an…

We consider higher order linear, uniformly elliptic equations with non-smooth coefficients in Banach-Sobolev spaces generated by weighted general Banach Function Space (BFS). Supposing boundedness of the Hardy-Littlewood Maximal and…

Let $\Gamma$ be a discrete icc subgroup of PSL(2,R) of infinite covolume. and let M denote the quotient of the unit disc by $\Gamma$. We prove that a Toeplitz operator with $\Gamma$-invariant symbol f in C(M) is Brauer Fredholm if its…

We study the generalized fractional linear problem $D^{\nu}_{a+*} f(x) =A(x)f(x)+g(x)$, where $D^{\nu}$ is an arbitrary mixture of Caputo derivatives of order at most one and $A(x)$ a family of operators in a Banach space generating…

The index of a pseudo B-Fredholm operator will be defined and generalize the usual index of a B-Fredholm operator. This concept will be used to extend some known results in Fredholm's theory. Among other results, the nullity, the…

Let A denote the C*algebra of bounded operators on L2(R) generated by: (i) all multiplications a(M) by functions a\in C[-\infty,+\infty], (ii) all multiplications by 2\pi-periodic continuous functions and (iii) all Fourier multipliers…

In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…

We provide Fredholm conditions for compatible differential operators on certain Lie manifolds (that is, on certain possibly non-compact manifolds with nice ends). We discuss in more detail the case of manifolds with cylindrical, hyperbolic,…

This note relates the notion of a discrete-spectrum family of Fredholm operators, recently introduced by N. Ivanov in arXiv:2111.15081, with the classical continuity properties in the space of operators.

$G$-operators, a class of differential operators containing the differential operators of minimal order annihilating Siegel's $G$-functions, satisfy a condition of moderate growth called Galochkin condition, encoded by a $p$-adic quantity,…

An elliptic equation of order $2m$ with general nonlocal boundary-value conditions, in a plane bounded domain $G$ with piecewise smooth boundary, is considered. Generalized solutions belonging to the Sobolev space $W_2^m(G)$ are studied.…

We investigate a large class of linear boundary value problems for the general first-order one-dimensional hyperbolic systems in the strip $[0,1]\times\R$. We state rather broad natural conditions on the data under which the operators of…

For a densely defined self-adjoint operator $\mathcal{H}$ in Hilbert space $\mathcal{F}$ the operator $\exp(-it\mathcal{H})$ is the evolution operator for the Schr\"odinger equation $i\psi'_t=\mathcal{H}\psi$, i.e. if $\psi(0,x)=\psi_0(x)$…