Related papers: Contributions to infinite dimensional geometry and…
The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent…
In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.
These three topics are an attempt to explicate some curiosities of the inverse problem of representation theory (i.e. having a set of operators to describe the "correct" algebraic object, which is represented by them) on simple examples…
We construct a new family of infinite-dimensional quasi-graded Lie algebras on hyperelliptic curves. We show that constructed algebras possess infinite number of invariant functions and admit a decomposition into the direct sum of two…
Infinite-dimensional algebra of all infinitesimal transformations of solutions of the self-dual Yang-Mills equations is described. It contains as subalgebras the infinite-dimensional algebras of hidden symmetries related to gauge and…
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite…
The article provides an introduction to infinite-dimensional differential calculus over topological fields and surveys some of its applications, notably in the areas of infinite-dimensional Lie groups and dynamical systems.
The thesis comprises three chapters. Chapter 1 investigates generalizations of the theorem of Fatou for convolution type integral operators with general approximate identities. It is introduced $\lambda(r)$-convergence, which is a…
The subject of Chapter 1 is GKK $\tau$-matrices and related topics. Chapter 2 is devoted to boundedly invertible collections of matrices, with applications to operator norms and spline approximation. Various structured matrices (Toeplitz,…
Filling functions are asymptotic invariants of finitely presentable groups; the seminal work on the subject is by M.Gromov. They record features of combinatorial homotopy discs (van Kampen diagrams) filling loops in Cayley 2-complexes.…
This is author's Habilitation Thesis (Dr. Sci. dissertation) submitted at the beginning of September 2004. It is written in Russian and is posted due to the continuing requests for the manuscript. The content: 1. Introduction, 2. Nonlinear…
We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the N-extented self-dual super Yang-Mills equations for general N\leq4 by using the supertwistor correspondence.…
A detailed presentation of the results obtained during my Ph.D. research. The main investigations concern explicit descriptions of classes of finite dimensional pointed Hopf algebras and their quasi-isomorphism types.
We give an introduction to the realisation theory for infinite-dimensional systems. That is, we show that for any function $G$, analytic and bounded in the right half of the complex plane, there exists operators $A,B,C$ such that…
Integration is the final key step when turning an infinitesimal argument into a result applicable to quantities of finite size. Conceptually, it is about combining infinitesimal contributions to a finite whole. We make a first step towards…
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
This paper is the second part of our series of works to establish $L^2$ estimates and existence theorems for the $\overline{\partial}$ operators in infinite dimensions. In this part, we consider the most difficult case, i.e., the underlying…
The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…
This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…
Let $A$ be a graded C*-algebra. We characterize Kasparov's K-theory group $\hat{K}_0(A)$ in terms of graded *-homomorphisms by proving a general converse to the functional calculus theorem for self-adjoint regular operators on graded…