Related papers: Variable Exponent Fock Spaces
We categorify various Fock space representations on the algebra of symmetric functions via the category of polynomial functors. In a prequel, we used polynomial functors to categorify the Fock space representations of type A affine Lie…
The notion of the eigenvalue problem in the Fock space with polynomial eigenfunctions is introduced. This problem is classified by using the finite-dimensional representations of the $\mathfrak{sl}(2)$-algebra in Fock space. In the complex…
A deformation of the Fock space based on the finite difference replacement for the derivative is introduced. The deformation parameter is related to the dimension of the finite analogue of the Fock space.
We describe a very general (nonlinear) Fredholm theory for a new class of ambient spaces, called polyfolds. The basic feature of these new spaces is that in general they may have locally varying dimensions. These new spaces are needed for a…
We study sampling and interpolation arrays with multiplicities for the spaces P_k of holomorphic polynomials of degree at most k. We find that the geometric conditions satisfied by these arrays are in accordance with the conditions…
We introduce and study a general notion of polynomial functor from a small monoidal symmetric category whose unit is an initial object and give a classification result of polynomial functors of degree smaller of equal to n modulo those of…
This paper is devoted to a systematic study and characterizations of the fundamental notions of variational and strong variational convexity for lower semicontinuous functions. While these notions have been quite recently introduced by…
We explore the Bohr inequality involving the Fourier transforms of complex valued integrable and square integrable functions defined on a second countable compact topological group. We also investigate the connection of the Bohr phenomenon…
We introduce \`a la Vasilevski the weighted poly-Bergman spaces in the unit disc and provide concrete orthonormal basis and give close expression of their reproducing kernel. The main tool in the description if these spaces is the so-called…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
We discuss the concepts of fine and coarse moduli spaces in the context of finite dimensional algebras over algebraically closed fields. In particular, our formulation of a moduli problem and its potential strong or weak solution is adapted…
This paper addresses the topological structures induced on vector spaces by convex modulars that do not satisfy the $\Delta_2$ condition, with particular focus on their applications to variable exponent spaces such as \( \ell^{(p_n)} \) and…
In this paper we examine the existence of bicomplexified inverse Fourier transform as an extension of its complexified inverse version within the region of convergence of bicomplex Fourier transform. In this paper we use the idempotent…
Inspired by our previous work on the boundedness of Toeplitz operators, we introduce weak BMO and VMO type conditions, denoted by BWMO and VWMO, respectively, for functions on the open unit disc of the complex plane. We show that the…
The intuitionistic implication and hence the notion of function space in constructive disciplines is both non-geometric and impredicative. In this paper we try to solve both of these problems by first introducing weak exponential objects as…
The first part of this paper surveys several results on the lattice structure of variable exponent Lebesgue function spaces (or Nakano spaces) $\lpv$. In the second part strictly singular and disjointly strictly singular operators between…
In [Y.~K.~Hu, K.~A.~Kopotun, X.~M.~Yu, Constr. Approx. 2000], the authors have obtained a characterization of best $n$-term piecewise polynomial approximation spaces as real interpolation spaces between $L^p$ and some spaces of bounded…
We give a moderately motivated exposition of exponentiable locales and the construction of exponentials in $\textsf{Loc}$, without assuming prior knowledge of exponential topological spaces or continuous posets.
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
We give different types of new characterizations for the boundedness and essential norms of generalized weighted composition operators between Zygmund type spaces. Consequently, we obtain new characterizations for the compactness of such…