相关论文: Operators on Spaces Generated by Infinite Dimensio…
Maps are polygonal cellular networks on Riemann surfaces. This paper analyzes the construction of closed form general representations for the enumerative generating functions associated to maps of fixed but arbitrary genus. The method of…
In this work we study the framework of mathematical morphology on simplicial complex spaces. Simplicial complexes are widely used to represent multidimensional data, such as meshes, that are two dimensional complexes, or graphs, that can be…
Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This…
Suppose $(C_t)_{t\geq0}$ is the composition semigroup induced by a one-parameter semigroup $(\varphi_t)_{t\geq0}$ of analytic self-maps of the unit disk. The main purpose of the paper is to investigate the spectrum of the infinitesimal…
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…
This paper deals with some special integral transforms of Bargmann-Fock type in the setting of quaternionic valued slice hyperholomorphic and Cauchy-Fueter regular functions. The construction is based on the well-known Fueter mapping…
The paper considers bounded linear radial operators on the polyanalytic Fock spaces $\mathcal{F}_n$ and on the true-polyanalytic Fock spaces $\mathcal{F}_{(n)}$. The orthonormal basis of normalized complex Hermite polynomials plays a…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
The first part of this thesis proposes a general approach to infinite dimensional non-Gaussian analysis, including the Poissonian case. In particular distribution theory is developed. Using appropriate integral transformations, generalized…
We consider the recursion operators with nonlocal terms of special form for evolution systems in (1+1) dimensions, and extend them to well-defined operators on the space of nonlocal symmetries associated with the so-called universal Abelian…
Quadratic harnesses are time-inhomogeneous Markov polynomial processes with linear conditional expectations and quadratic conditional variances with respect to the past-future filtrations. Typically they are determined by five numerical…
Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…
In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…
Non-Archimedean mathematics is an approach based on fields which contain infinitesimal and infinite elements. Within this approach, we construct a space of a particular class of generalized functions, ultrafunctions. The space of…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
In this paper, we enlarge the space of uniformly supported pseudo-differential operators on some groupoids by considering kernels satisfying certain asymptotic estimates. We show that such enlarged space contains the compact parametrix, and…
We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of…
We study multiplication as well as Nemytskij operators in anisotropic vector-valued Besov spaces $B^{s, \omega}_p$, Bessel potential spaces $H^{s, \omega}_p$, and Sobolev-Slobodeckij spaces $W^{s, \omega}_p$. Concerning multiplication we…
By means of the Bessel operator a polynomial sequence is constructed to which several properties are given. Among them, its explicit expression, the connection with the Euler numbers, its integral representation via the Kontorovich-Lebedev…