Related papers: Holomorphic Sobolev spaces and the generalized Seg…

For a given group $G$, it is natural to ask whether one can classify all isometric $G$-actions on Gromov hyperbolic spaces. We propose a formalization of this problem utilizing the complexity theory of Borel equivalence relations. In this…

A generalization of the Hartogs theorem is proved for a class of Tubes structures. We assume that the intervening commutative Lie algebra admits at least a number of globally solvable generators greater or equal to the structure…

Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant geometric K-homology groups K^G_*(X), using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural…

Coorbit space theory is an abstract approach to function spaces and their atomic decompositions. The original theory developed by Feichtinger and Gr{\"o}chenig in the late 1980ies heavily uses integrable representations of locally compact…

We establish a concentration-compactness principle for the Sobolev space $W^{2,p(\cdot)}(\Omega)\cap W_0^{1,p(\cdot)}(\Omega)$ that is a tool for overcoming the lack of compactness of the critical Sobolev imbedding. Using this result we…

In this paper we introduce generalized pseudo-quadratic forms and develope some theory for them. Recall that the codomain of a $(\sigma,\varepsilon)$-quadratic form is the group $\overline{K} := K/K_{\sigma,\varepsilon}$, where $K$ is the…

Let G be a complex semisimple Lie group, K a maximal compact subgroup and V an irreducible representation of K. Denote by M the unique closed orbit of G in P(V) and by O its image via the moment map. For any measure on M we construct a map…

We study the pullback theorem of Sobolev mappings on Carnot groups via mollification of mappings. With the pullback theorem we extend the classical result proved by Xiangdong Xie : Rigidity of Sobolev mappings $W^{1,p}(G_1;G_2)$ for…

We prove a compactness theorem for embedded measured hyperbolic Riemann surface laminations in a compact almost complex manifold $(X, J)$. To prove compactness result, we show that there is a suitable topology on the space of measured…

In this paper we estimate the Sobolev embedding constant on general noncompact Lie groups, for sub-Riemannian inhomogeneous Sobolev spaces endowed with a left invariant measure. The bound that we obtain, up to a constant depending only on…

In this paper, we consider a generalized two component Camassa-Holm system. Based on local well-posedness results and lifespan estimates, we establish sharpness of continuity on the data-to-solution map by showing that it is not uniformly…

Every topological group $G$ has some natural compactifications which can be a useful tool of studying $G$. We discuss the following constructions: (1) the greatest ambit $S(G)$ is the compactification corresponding to the algebra of all…

We introduce new classes of right quaternionic Hilbert spaces of Bargmann-Fock type $\mathcal{GB}_{m}^{2}(\mathbb{H})$, labeled by nonnegative integer $m$, generalizing the so-called slice hyperholomorphic Bargmann-Fock space introduced…

We study the action of Bogoliubov transformations on admissible generalized one-particle density matrices arising in Hartree-Fock-Bogoliubov theory. We show that the orbits of this action are reductive homogeneous spaces, and we give…

This paper is a self-contained presentation of certain aspects of the theory of weighted Sobolev spaces and elliptic operators on non-compact Riemannian manifolds. Specifically, we discuss (i) the standard and weighted Sobolev Embedding…

Let a compact group G act on real or complex C*-algebras A and B, with A separable and B sigma-unital. We express the G-equivariant Kasparov groups KK_n(A,B) by algebraic K-groups of a certain additive category.

We study properties of a map from a certain unitary group in $n$ variables to a related unitary group in $\binom{n}{k}$ variables. We explain how it gives rise to a map between canonical models of Shimura varieties and we prove that it…

We study topological groups of monotonic autohomeomorphisms on a generalized ordered space $L$. We find a condition that is necessary and sufficient for the set of all monotonic autohomeomorphisms on $L$ along with the function composition…

Let $(X, \omega)$ be a compact symplectic manifold and $L$ be a Lagrangian submanifold. Suppose $(X, L)$ has a Hamiltonian $S^1$ action with moment map $\mu$. Take an invariant $\omega$-compatible almost complex structure, we consider…

We study several connected problems of holomorphic function spaces on homogeneous Siegel domains. The main object of our study concerns weighted mixed norm Bergman spaces on homogeneous Siegel domains of type II. These problems include:…