Related papers: Weierstrass Semigroups From a Tower of Function Fi…
Second order equations of the form $z'' + A_0 z + D z'=0$ in an abstract Hilbert space are considered. Such equations are often used as a model for transverse motions of thin beams in the presence of damping. We derive various properties of…
Let X be an algebraic curve, defined over a perfect field, and G a divisor on X. If X has sufficiently many points, we show how to construct a divisor D on X such that l(2D-G)=0, of essentially any degree such that this is compatible the…
We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…
Frobenius problem and its many generalizations have been extensively studied in several areas of mathematics. We study semigroups of totally positive algebraic integers in totally real number fields, defining analogues of the Frobenius…
We remove the global quotient presentation input in the theory of windows in derived categories of smooth Artin stacks of finite type. As an application, we use existing results on flipping of strata for wall-crossing of Gieseker…
This mostly expository article explores recent developments in the relations between the three objects in the title from an algebro-combinatorial perspective. We prove a formula for Whittaker functions of a real semisimple group as an…
We fix a monic polynomial $f(x) \in \mathbb F_q[x]$ over a finite field and consider the Artin-Schreier-Witt tower defined by $f(x)$; this is a tower of curves $\cdots \to C_m \to C_{m-1} \to \cdots \to C_0 =\mathbb A^1$, with total Galois…
Let $F_\infty=\mathbb{F}_q(\!(1/T)\!)$ be the completion of $\mathbb{F}_q(T)$ at $1/T$. We develop a theory of Fourier expansions for harmonic cochains on the edges of the Bruhat-Tits building of $\mathrm{PGL}_r(F_\infty)$, $r\geq 2$,…
For smooth bounded open sets in euclidean space, we construct corresponding contractive linear extension operators for the space of continuous functions which preserve regularity of functions in the domain of the Robin Laplacian. We also…
This paper studies three results that describe the structure of the super-coinvariant algebra of pseudo-reflection groups over a field of characteristic $0$. Our most general result determines the top component in total degree, which we…
Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that…
The introduction of abstract Friedrichs operators in 2007-an operator-theoretic framework for studying classical Friedrichs operators has led to significant developments in the field, including results on well-posedness, multiplicity, and…
We study the structure of the vector space of Drinfeld quasi-modular forms for congruence subgroups. We provide representations as polynomials in the false Eisenstein series with coefficients in the space of Drinfeld modular forms (the…
We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and generators of the special unitary group…
We provide a new lower bound for the dimension of the moduli space of smooth pointed curves with prescribed Weierstrass semigroup at the marked point, derived from the Deligne-Greuel formula and Pinkham's equivariant deformation theory.…
Let us consider a generalized Artin-Schreier algebraic function field extension $F$ of the rational function field $\F_{p^n}(x)$ defined over the finite field extension $K=\F_{p^n}$ of the prime field $\F_p$. We assume that $K$ is…
We study differentiability properties of Zygmund functions and series of Weierstrass type in higher dimensions. While such functions may be nowhere differentiable, we show that, under appropriate assumptions, the set of points where the…
We develop a theory of measures, differential forms and Fourier tramsforms on some infinite-dimensional real vector spaces by generalizing the following two constructions: (a) The construction of the semiinfinite wedge power of a Tate…
We study spectral properties of Schr\"odinger operators with $\delta$-interactions on a semi-axis by using the theory of boundary triplets and the corresponding Weyl functions. We establish a connection between spectral properties…
Convoluted $C$-cosine functions and semigroups in a Banach space setting extending the classes of fractionally integrated $C$-cosine functions and semigroups are systematically analyzed. Structural properties of such operator families are…