Related papers: Dilation theory in finite dimensions: the possible…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
In this work, we propose a convenient framework for infinite-dimensional analysis (including both real and complex analysis in infinite dimensions), in which differentiation (in some weak sense) and integration operations can be easily…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
We develop a theory of holomorphic differentials on a certain class of non-compact Riemann surfaces obtained by opening infinitely many nodes.
This is a brief introduction to control theory in finite-dimensional spaces. The material is partly based on my lectures for the Master 1 program in Math\'ematiques et applications at Sorbonne University, delivered over the past few years.…
We will give an outline of the main results in our recent AMS Memoir, and include some new results, exposition and open problems. In that memoir we developed a general dilation theory for operator valued measures acting on Banach spaces…
We present a completely new structure theoretic approach to the dilation theory of linear operators. Our main result is the following theorem: if $X$ is a super-reflexive Banach space and $T$ is contained in the weakly closed convex hull of…
In this preprint we present an outline of the multidimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvability by radicals, by…
We present a set-theoretic version of some basic dilation results of operator theory. The results we have considered are Wold decomposition, Halmos dilation, Sz. Nagy dilation, inter-twining lifting, commuting and non-commuting dilations,…
The spectral theory for operator pencils and operator differential-algebraic equations is studied. Special focus is laid on singular operator pencils and three different concepts of singularity of operator pencils are introduced. The…
The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…
We formulate and prove finite dimensional analogs for the classical Balian-Low theorem, and for a quantitative Balian-Low type theorem that, in the case of the real line, we obtained in a previous work. Moreover, we show that these results…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
We introduce the notion of almost finite dimensionality of algebras and study its connection with the classical finiteness conditions.
We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…
We apply Lax-Milgram theorem to characterize scalable and piecewise scalable frame in finite and infinite-dimensional Hilbert spaces. We also introduce a method for approximating the inverse frame operator using finite-dimensional linear…
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…
We give infinite dimensional and finite dimensional examples of $F-$fold Lie superalgebras. The finite dimensional examples are obtained by an inductive procedure from Lie algebras and Lie superalgebras.
Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over…
The addition relation for the Riemann theta functions and for its limits, which lead to the appearance of exponential functions in soliton type equations is discussed. The presented form of addition property resolves itself to the…