Related papers: A new generalization of Browder degree

We associate to any endomorphism of the punctured affine space over some field an element in the Witt group of the base field that we call degree. We use this degree to give a counter-example to a question on unimodular rows

We study the computational difficulty of the problem of finding fixed points of nonexpansive mappings in uniformly convex Banach spaces. We show that the fixed point sets of computable nonexpansive self-maps of a nonempty, computably weakly…

This paper is an account (without proofs) of the results of our work "Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications", funct-an/9311001. The Section 9 establishing a connection between variational…

For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…

In this work, using a new geometrical approach we study to the existence of the fixed-point of mappings that independence of the smoothness, and also of their single-values or multi-values. This work proved the theorems that generalize in…

The main topic is the development of a Fredholm theory in a new class of spaces called M-polyfolds. In the subsequent Volume II the theory will be generalized to an even larger class of spaces called polyfolds, which can also incorporate…

A broader class of Hardy spaces and Lebesgue spaces have been introduced recently on the unit circle by considering continuous $\|.\|_1$-dominating normalized gauge norms instead of the classical norms on measurable functions and a Beurling…

We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…

This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of nonorientable surfaces into which such graphs may be embedded. In a previous paper by the authors, the problem of…

The theory of modular flow has proved extremely useful for applying thermodynamic reasoning to out-of-equilibrium states in quantum field theory. However, the standard proofs of the fundamental theorems of modular flow use machinery from…

A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the…

We investigate the most general N=1 graded extension of the Poincare algebra, and find the corresponding supersymmetry transformations and the associated superspaces. We find that the supersymmetry for which {Q,Q} = P is not special, and in…

We design an abstract setting for the approximation in Banach spaces of operators acting in duality. A typical example are the gradient and divergence operators in Lebesgue--Sobolev spaces on a bounded domain. We apply this abstract setting…

This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…

We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…

In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…

Let $A\in\mathcal{B}(X)$, $B\in\mathcal{B}(Y)$ and $C\in\mathcal{B}(Y,X)$ where $X$ and $Y$ are infinite Banach or Hilbert spaces. Let $M_{C}=\begin{pmatrix} A & C\cr 0 & B \end{pmatrix}$ be $2\times 2$ upper triangular operator matrix…

We introduce a new definition of topological degree for a meaningful class of operators which need not be continuous. Subsequently, we derive a number of fixed point theorems for such operators. As an application, we deduce a new existence…

We calculate the degree of the algebra of covariants $\mathcal{C}_d$ for binary $d$-form. Also, for the degree we obtain its integral representation and asymptotic behavior.

The linear isometries between weighted Banach spaces of continuous functions are considered. Some of well known theorems on isometries between spaces of continuous functions are proved and stated, but all they are in an appropriate form. In…