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By analogy with the classical definition, a Norm Hilbert space $E$ is defined as a Banach space over a valued field $K$ in which each closed subspace has an orthocomplement. In the rank one case (that is, the value group as well as the set…
We develop a representation of the second kind for certain Hardy classes of solutions to nonhomogeneous Cauchy-Riemann equations and use it to show that boundary values in the sense of distributions of these functions can be represented as…
This paper builds upon our recent work, published in Lett. Math. Phys., 112: 94, 2022, where we established that the integrable Volterra lattice on a free associative algebra and the whole hierarchy of its symmetries admits a quantisation…
Many recently proposed gradient projection algorithms with inertial extrapolation step for solving quasi-variational inequalities in Hilbert spaces are proven to be strongly convergent with no linear rate given when the cost operator is…
We introduce the good Hilbert functor and prove that it is algebraic. This functor generalizes various versions of the Hilbert moduli problem, such as the multigraded Hilbert scheme and the invariant Hilbert scheme. Moreover, we generalize…
We discuss the quantization of an unstable field through the construction of a "one-particle Hilbert space." The system considered here is a neutral scalar field evolving over a globally hyperbolic static spacetime and subject to a…
Invertible processes are central to functional time series analysis, making the estimation of their defining operators a key problem. While asymptotic error bounds have been established for specific ARMA models on $L^2[0,1]$, a general…
In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimensions. It is shown that existence theorems for scalar/vector…
The Hodge equations for 1-forms are studied on Beltrami's projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for…
This paper is devoted to studying abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces. First, we prove the existence of unique local mild solutions and show their regularity. Second, we show the regular…
In this note we define and study a Hilbert space-valued stochastic integral of operator-valued functions with respect to Hilbert space-valued measures. We show that this integral generalizes the classical Ito stochastic integral of adapted…
We give an explicit description of the matrix associated to the $U_p$ operator acting on spaces of overconvergent Hilbert modular forms over totally real fields. Using this, we compute slopes for weights in the centre and near the boundary…
We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being…
This paper is concerned with frame decompositions of $\alpha$-modulation spaces. These spaces can be obtained as coorbit spaces for square-integrable representations of the affine Weyl-Heisenberg group modulo suitable subgroups. The theory…
In a separable Hilbert space, we study supercontractivity and ultracontractivity properties for a transition semigroups associated with a stochastic partial differential equations. This is done in terms of exponential integrability of…
In this paper we generalise the notion of Drinfeld modular form for the group $\Gamma$ := GL2(Fq[$\theta$]) to a vector-valued setting, where the target spaces are certain modules over positive characteristic Banach algebras over which are…
In this paper we analyze two different functional formulations of classical mechanics. In the first one the Jacobi fields are represented by bosonic variables and belong to the vector (or its dual) representation of the symplectic group. In…
We consider mod p Hilbert modular forms associated to a totally real field of degree d in which p is unramified. We prove that every such form arises by multiplication by partial Hasse invariants from one whose weight (a d-tuple of…
The aim of this paper is to present an explicit reduction algorithm for Hilbert modular groups over arbitrary totally real number fields. An implementation of the algorithm is available to download from [19]. The exposition is…
We define localized modulation maps and modulation spaces of symbols suited to the study of Rieffel's deformation quantization pseudodifferential calculus. They are used to generate Hilbert space representations for the quantized…