Related papers: On regular families of cardinal interpolators and …
We study the boundedness of families of algebraic flat connections with bounded irregularity. As an application, we study the boundedness of families of holonomic $D$-modules with dominated characteristic cycles.
Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint…
We mainly investigate model of set theory with restricted choice, e.g., ZF + DC + "the family of countable subsets of lambda is well ordered for every lambda" (really local version for a given lambda). In this frame much of pcf theory can…
If $f\in \{f\in L^p(\mathbb{R}): f(x)=\int_{-\pi}^{\pi}e^{ix\xi}d\beta(\xi), \beta\in B.V.([-\pi,\pi]) \}$, then $f$ is determined by its samples on the integers by taking an appropriate limit. Specifically, $\| f - L_{\phi_\alpha}f…
We establish a link between Fourier optics and a recent construction from the machine learning community termed the kernel mean map. Using the Fraunhofer approximation, it identifies the kernel with the squared Fourier transform of the…
A ballean is a set $X$ endowed with some family $\F$ of its subsets, called the balls, in such a way that $(X,\F)$ can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal $\kappa$, we define $\F$…
We investigate multi-graded Gorenstein semigroup algebras associated with an infinite family of reflexive lattice simplices. For each of these algebras, we prove that their multigraded Poincar\'e series is rational. Our method of proof is…
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…
By applying new functional analysis tools in the framework of Fourier interpolation formulas, such as sc-Fredholm operators and Schauder frames, we are able to improve and refine several properties of these aforementioned formulas on the…
This paper considers the problem of assumptions refinement in the context of unrealizable specifications for reactive systems. We propose a new counterstrategy-guided synthesis approach for GR(1) specifications based on Craig's…
Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
We introduce a model-theoretic characterization of Magidor cardinals, from which we infer that Magidor filters are beyond ZFC-inconsistency
We mostly survey results concerning the $L^2$ boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.
This paper is a continuation of the research of our previous work and considers quaternionic generalized Carath\'eodory functions and the related family of generalized positive functions. It is addressed to a wide audience which includes…
The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…
This article pertains to interpolation of Sobolev functions at shrinking lattices $h\mathbb{Z}^d$ from $L_p$ shift-invariant spaces associated with cardinal functions related to general multiquadrics,…
In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of singularities at the origin, such as $x^\alpha$ for $\alpha \in…
We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality.…
We study a family of Fourier integral operators, by allowing their symbols to satisfy a multi-parameter differential inequality. We extend the sharp L^p-result obtained by Seeger, Sogge and Stein to product spaces.