Related papers: Approximation and Interpolation in Kolmogorov-type…

In the search for hypercomplex analytic functions on the half-plane, we review the construction of induced representations of the group G=SL(2,R). Firstly we note that G-action on the homogeneous space G/H, where H is any one-dimensional…

Using an original method, we find the algebra of generalized symmetries of a remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation, which is also called the Kolmogorov equation and is singled out within the entire class of…

Extending and unifying concepts extensively used in the literature, we introduce the notion of approximable interpolation sets for algebras of functions on locally compact groups, especially for weakly almost periodic functions and for…

Let $G$ be a noncompact connected Lie group, denote with $\rho$ a right Haar measure and choose a family of linearly independent left-invariant vector fields $\mathbf{X}$ on $G$ satisfying H\"ormander's condition. Let $\chi$ be a positive…

This paper addresses a novel weighted Riesz--Kolmogorov theorem and the extrapolation of multilinear compact operators in the context of weighted variable Lebesgue spaces. We establish the latter result via our Riesz--Kolmogorov theorem…

We give a criterion for the Kostant-Kirillov form on an adjoint orbit in a real semisimple Lie group to be exact. We explicitly compute the second cohomology of all the nilpotent adjoint orbits in every complex simple Lie algebras.

The research monograph gives the first systematic exposition of the elliptic (scalar and matrix) operators theory and elliptic boundary-value problems in the scales of Hilbert spaces of H\"ormander of the functions/distributions of…

Given $E_0, E_1, F_0, F_1, E$ rearrangement invariant function spaces, $a_0$, $a_1$, $b_0$, $b_1$, $b$ slowly varying functions and $0< \theta_0<\theta_1<1$, we characterize the interpolation spaces $$(\overline{X}^{\mathcal…

We deal with a problem of the reconstruction of any holomorphic function $f$ on the unit ball of $\mathbb{C}^2$ from its restricions on a union of complex lines. We give an explicit formula of Lagrange interpolation's type that is…

A new notion of a Hausdorff-type operator on function spaces over domains in Euclidean spaces is introduced, and a sufficient condition for the boundedness of this operator on Sobolev spaces is proved. It is shown that this condition cannot…

We describe the (equivariant) intersection cohomology of certain moduli spaces ("framed Uhlenbeck spaces") together with some structures on them (such as e.g.\ the Poincar\'e pairing) in terms of representation theory of some vertex…

We study the interpolation Macdonald functions, remarkable inhomogeneous generalizations of Macdonald functions, and a sequence $A^1, A^2, \ldots$ of commuting operators that are diagonalized by them. Such a sequence of operators arises in…

We give a generalization of the Hodge operator to spaces $(V,h)$ endowed with a hermitian or symmetric bilinear form $h$ over arbitrary fields, including the characteristic two case. Suitable exterior powers of $V$ become free modules over…

Motivated by recent results on the (possibly conditional) regularity for time-dependent hypoelliptic equations, we prove a parabolic version of the Poincar\'e inequality, and as a consequence, we deduce a version of the classical Moser…

We prove a number of results on integrability and extendability of Lie algebras of unbounded skew-symmetric operators with common dense domain in Hilbert space. By integrability for a Lie algebra $\mathfrak{g}$, we mean that there is an…

We give a Orlik-Solomon type presentation for the cohomology ring of arrangements in a non-compact abelian Lie group. The new insight consists in comparing arrangements in different abelian groups. Our work is based on the Varchenko-Gelfand…

It is known that every function with a finite support over a given field can be interpolated by means of the Lagrangian polynomial. The question is if a similar interpolation is possible if one considers a unitary ring or a Boolean algebra…

A quasi-representation of a group is a map from the group into a matrix algebra (or similar object) that approximately satisfies the relations needed to be a representation. Work of many people starting with Kazhdan and Voiculescu, and…

We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds generate the cohomology groups of degree…

In this paper, we give a new series of coboundary operators of Hom-Lie algebras. And prove that cohomology groups with respect to coboundary operators are isomorphic. Then, we revisit representations of Hom-Lie algebras, and generalize the…