Related papers: Invitation to higher local fields, Part I, section…
This paper summarizes our rather lengthy paper, "Algebra of the Infrared: String Field Theoretic Structures in Massive ${\cal N}=(2,2)$ Field Theory In Two Dimensions," and is meant to be an informal, yet detailed, introduction and summary…
We provide a detailed description of the model Hilbert space $L^2(\bbR; d\Sigma; \cK)$, were $\cK$ represents a complex, separable Hilbert space, and $\Sigma$ denotes a bounded operator-valued measure. In particular, we show that several…
This work introduces adelic constructions of direct images of differentials and symbols in the two-dimensional case in the relative situation. In particular, reciprocity laws for relative residues of differentials and symbols are stated and…
We introduce a continuous scale of Hilbert spaces of entire functions $P_\beta (D)$ for a bounded convex domain $D$ on the complex plane. For the parameters $\beta \in (\frac 12;\frac 32)$ a complete description of the spaces of Borel…
In this paper we give several expressions of spectral radius of a bounded operator on a Hilbert space, in terms of iterates of Aluthge transformation, numerical radius and the asymptotic behavior of the powers of this operator. Also we…
We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local…
A new formalism to express and operate on diversity measures of qualitative variables, built in a Hilbert space, is presented. The abstract character of the Hilbert space naturally incorporates the equivalence between qualitative variables…
The two reference lists contain 54/22 references of papers and preprints concerned with the theory and/or various applications of Hilbert modules over Hilbert $*$-algebras and over (non-self-adjoint) operator algebras. They are far from…
A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…
This is a survey of results on the Hilbert property of algebraic varieties, and variants of it.
The aim of this work is to provide a construction of generalized local symbols on algebraic curves as morphisms of group schemes. From a closed point of a complete, irreducible and non-singular curve $C$ over a perfect field $k$ as the only…
The Hilbert scheme of projective 3-folds of codimension 3 or more that are linear scrolls over the projective plane or over a smooth quadric surface or that are quadric or cubic fibrations over the projective line is studied. All known such…
This article aims to explore the most recent developments in the study of the Hilbert matrix, acting as an operator on spaces of analytic functions and sequence spaces. We present the latest advances in this area, aiming to provide a…
In this presentation we shall deal with some aspects of the theory of Hilbert functions of modules over local rings, and we intend to guide the reader along one of the possible routes through the last three decades of progress in this area…
Several notions of multiplicativity are introduced for forms of degree $d\geq 3$ over a field of characteristic 0 or greater than d. Examples of multiplicative and strongly multiplicative forms of higher degree are given. Conditions…
In the paper, the authors first inductively establish explicit formulas for derivatives of the arc sine function, then derive from these explicit formulas explicit expressions for a family of Bell polynomials related to the square function,…
We study the explicit formula of Euler numbers and polynomials of higher order
Let $K$ be an unramified extension of $\mathbb{Q}_2$ and $\mu_{2^n}$ the group of $2^n$-th root of unity for a fixed integer $n\geqslant 2$. In this paper, we give an explicit formula for the $\mu_{2^n}$-valued Hilbert symbol over $K_n :=…
We talk about the image of the Hilbert map. We show the necessary and sufficient condition that the Hilbert map is surjective.
We present the $\textit{NumericalImplicitization}$ package for $\textit{Macaulay2}$, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This…