Related papers: Oversampling and Donoho-Logan type theorems in mod…

We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating…

This work is devoted to a vast extension of Sanov's theorem, in Laplace principle form, based on alternatives to the classical convex dual pair of relative entropy and cumulant generating functional. The abstract results give rise to a…

In this paper, we study the problem of direction of arrival estimation and model order selection for systems employing subarray sampling. Thereby, we focus on scenarios, where the number of active sources is not smaller than the number of…

Weak-to-Strong Generalization (W2SG), where a weak model supervises a stronger one, serves as an important analogy for understanding how humans might guide superhuman intelligence in the future. Promising empirical results revealed that a…

Contents (Part 1): 1.Derivation of Lorentz Invariance and Three Space Dimensions in Generic Field Theory (C D. Froggatt and H. B. Nielsen) 2.Unitary Representations, Noncompact Groups SO(q; d - q)...(N. Mankoc Borstnik, H. B. Nielsen and D.…

We construct a new class of two-dimensional field theories with target spaces that are finite multiparameter deformations of the usual coset G/H-spaces. They arise naturally, when certain models, related by Poisson-Lie T-duality, develop a…

Here we provide a unifying treatment of the convergence of a general form of sampling type operators, given by the so-called Durrmeyer sampling type series. In particular we provide a pointwise and uniform convergence theorem on…

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…

The object of this paper is to prove a version of the Beurling-Helson-Lowdenslager invariant subspace theorem for operators on certain Banach spaces of functions on a multiply connected domain in the complex plane. The norms for these…

We introduce Hilbertian Hardy--Sobolev spaces on tube domains over convex cones and develop their structural theory from a Fourier-analytic point of view. We first establish a Paley--Wiener type representation, which identifies these spaces…

The purpose of this paper is to make a comprehensive connection between the basic results and properties derived from the two kinds of topologies (namely the $(\epsilon,\lambda)-$topology introduced by the author and the stronger locally…

A Schroedinger type equation on the superspace R^{D|2n} is studied, which involves a potential inversely proportional to the negative of the osp(D|2n) invariant "distance" away from the origin. An osp(2,D+1|2n) dynamical supersymmetry for…

Continuous dually epi-translation invariant valuations on convex functions are characterized in terms of the Fourier-Laplace transform of the associated Goodey-Weil distributions. This description is used to obtain integral representations…

In dimension two, we investigate a free energy and the ground state energy of the Schr\"odinger-Poisson system coupled with a logarithmic nonlinearity in terms of underlying functional inequalities which take into account the scaling…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

It is shown that Paley-Wiener functions on Riemannian manifolds of bounded geometry can be reconstructed in a stable way from some countable sets of their inner products with certain distributions of compact support. A reconstruction method…

Let $k$ be a local field with valuation ring $O_k$ and residue field $\overline{k}$. We extend Hahn--Banach theorem for the class of seminormed $k$-vector spaces to several classes of locally convex spaces and subspaces over $k$, $O_k$, and…

The state space and observables for the leading order of the large-N theory are constructed. The obtained model ("theory of infinite number of fields") is shown to obey Wightman-type axioms (including invariance under boost transformations)…

We prove a local limit theorem, i.e. a central limit theorem for densities, for a sequence of independent and identically distributed random variables taking values on an abstract Wiener space; the common law of those random variables is…

We consider the space of tensor densities on the n-dimensional sphere with degree lambda (or, equivalently, of conformal densities with degree lambda). This space is a module over the group of diffeomorphisms, and consequently over the Lie…