Related papers: De Branges spaces and Fock spaces
We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable…
The goal is to review the notion of a complete Segal space and how certain categorical notions behave in this context. In particular, we study functoriality in complete Segal spaces via fibrations. Then we use it to define limits and…
We detail a new approach to the bosonic Fock representation of a complex Hilbert space V: our account places the bosonic Fock space S[V] between the symmetric algebra SV and its full antidual SV'; in addition to providing a context in which…
Norm equivalences between a function and its Hankel transform are studied both in the context of weighted Lebesgue spaces with power weights, and in Lorentz spaces. Boas'-type results involving real-valued general monotone functions are…
In this paper, we investigate the relation between the Deddens and spectral radius algebras of two bounded linear operators, noting a similarity between them. Additionally, we characterize the Deddens and spectral radius algebras related to…
A variation of the Zamolodchikov-Faddeev algebra over a finite dimensional Hilbert space $\mathcal{H}$ and an involutive unitary $R$-Matrix $S$ is studied. This algebra carries a natural vacuum state, and the corresponding Fock…
The quotient shape types of normed vectorial spaces(over the same field) with respect to Banach spaces reduce to those of Banach spaces. The finite quotient shape type of normed spaces is an invariant of the (algebraic) dimension, but not…
We compute the partition function for the $N=1$ spinning particle, including pictures and the large Hilbert space, and show that it counts the dimension of the BRST cohomology in two- and four-dimensional target space. We also construct a…
Non-Fock representations of the canonical commutation relations modeled over an infinite-dimensional nuclear space are constructed in an explicit form. The example of the nuclear space of smooth real functions of rapid decrease results in…
In this note, we describe the backward shift invariant subspaces for a large class of reproducing kernel Hilbert spaces. This class includes in particular de Branges-Rovnyak spaces (the non-extreme case) and the range space of co-analytic…
We study some important topological properties such as boundedness, compactness and essential norm of differences of weighted composition operators between Fock spaces
We prove a categorical duality between a class of abstract algebras of partial functions and a class of (small) topological categories. The algebras are the isomorphs of collections of partial functions closed under the operations of…
We construct the Heisenberg counterpart of a Clifford categorification. It is a modification of Khovanov's Heisenberg categorification. We express generators of the Heisenberg category as a complex of generators of the Clifford category.…
Bounded and compact product of Volterra type integral and composition operators acting between weighted Fock spaces are described. We also estimate the norms of these operators in terms of Berezin type integral transforms on the complex…
In this article, we study the properties of a class of functional spaces which arise from the investigation of nonlinear differential equations. We establish some integral inequalities then by applying these inequalities, we prove some…
We present the first example of the Selberg type zeta function for noncompact higher rank locally symmetric spaces. We study certain Selberg type zeta functions and Ruelle type zeta functions attached to the Hilbert modular group of a real…
The problem of characterizing normed ordered spaces which admit a representation in the algebraic, order and norm sense as a subspace of $C(X)$, the space of all continuous functions on a compact Hausdorff space is a classical problem that…
The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite dimensional superspaces, and construct superanalogs of the classical…
Hilbert evolution algebras generalize evolution algebras through a framework of Hilbert spaces. In this work we focus on infinite-dimensional Hilbert evolution algebras and their representation through a suitably defined weighted digraph.…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…