Related papers: Projection Theorems and Estimating Equations for P…

The operator splitting approach applied to the Navier-Stokes equations, gave rise to various numerical methods for the simulations of the dynamics of fluids. The separate work of Chorin and Temam on this subject gave birth to the so-called…

We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.

In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…

We study the stability of regularization by projection for solving linear inverse problems if the forward operator is given indirectly but specified via some input-output training pairs. We extend the approach in "Data driven regularization…

This paper studies projections of uniform random elements of (co)adjoint orbits of compact Lie groups. Such projections generalize several widely studied ensembles in random matrix theory, including the randomized Horn's problem, the…

A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…

Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

The classical arithmetic Grothendieck-Riemann-Roch theorem can be applied only to projective morphisms that are smooth over the complex numbers. In this paper we generalize the arithmetic Grothendieck-Riemann-Roch theorem to the case of…

The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a…

The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…

We consider the probability theory, and in particular the moment problem and universality theorems, for random groups of the sort of that arise or are conjectured to arise in number theory, and in related situations in topology and…

Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…

An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fej\'{e}r's theorem is proved for these series. The theory is applied to distributional solutions of Cauchy-Riemann equations to…

Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

The projection lemma (often also referred to as the elimination lemma) is one of the most powerful and useful tools in the context of linear matrix inequalities for system analysis and control. In its traditional formulation, the projection…

Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…

We present a maximal class of analytic functions, elements of which are in one-to-one correspondence with their asymptotic expansions. In recent decades it has been realized (B. Malgrange, J. Ecalle, J.-P. Ramis, Y. Sibuya et al.), that the…