Related papers: The inversion formula and holomorphic extension of…

We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the…

We study the rings of invariants for the indecomposable modular representations of the Klein four group. For each such representation we compute the Noether number and give minimal generating sets for the Hilbert ideal and the field of…

We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space $\Sigma_m=\{0,...,m-1\}^\N$ that are invariant under multiplication by integers. The results apply to the sets $\{x\in \Sigma_m: \forall\, k, \ x_k x_{2k}...…

With the help of the deformed Heisenberg algebra involving Klein operator, we construct the minimal set of linear differential equations for the (2+1)-dimensional relativistic field with arbitrary fractional spin, whose value is defined by…

In this paper we introduce reproducing kernel Hilbert spaces of polyanalytic functions of infinite order. First we study in details the counterpart of the Fock space and related results in this framework. In this case the kernel function is…

We give a uniform realization of the minimal representation of a double cover of the conformal group SO(2,n+1)_0 in the kernel of the wave operator on flat Minkowski space as a positive energy representation H^+ for n even and odd. Using…

The algebra of functions on kappa-Minkowski noncommutative spacetime is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction…

For the group O(p,q) we give a new construction of its minimal unitary representation via Euclidean Fourier analysis. This is an extension of the q = 2 case, where the representation is the mass zero, spin zero representation realized in a…

The $\Pi$-operator, also known as Ahlfors-Beurling transform, plays an important role in solving the existence of locally quasiconformal solutions of Beltrami equations. In this paper, we first construct the $\Pi$-operator on a general…

An upper bound of the variation of argument of a holomorphic function along a curve on a Riemann surface is given. This bound is expressed through the Bernstein index of the function multiplied by a geometric constant. The Bernstein index…

We realize all irreducible unitary representations of the group $\mathrm{SO}_0(n+1,1)$ on explicit Hilbert spaces of vector-valued $L^2$-functions on $\mathbb{R}^n\setminus\{0\}$. The key ingredient in our construction is an explicit…

We find an explicit integral formula for the eigenfunctions of a fourth order differential operator against the kernel involving two Bessel functions. Our formula establishes the relation between K-types in two different realizations of the…

A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of…

Let $F$ be a non-archimedean local field, of characteristic 0. Let $V$ be a finite dimensional vector space over $F$ and $q$ be a non-degenerate quadratic form on $V$. Denote $G$ the special orthogonal group of $(V,q)$. Let $W$ a…

We count the connected components in the moduli space of PU(p,q)-representations of the fundamental group for a closed oriented surface. The components are labelled by pairs of integers which arise as topological invariants of the flat…

Let $G$ be a reductive Lie group and ${\mathcal O}$ the coadjoint orbit of a hyperbolic element of ${\frak g}^*$. By $\pi$ is denoted the unitary irreducible representation of $G$ associated with ${\mathcal O}$ by the orbit method. We give…

We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gr\"obner basis for the Hilbert ideal and…

Let T be a C_{\cdot 0}-contraction on a Hilbert space H and S be a non-trivial closed subspace of H. We prove that S is a T-invariant subspace of H if and only if there exists a Hilbert space D and a partially isometric operator \Pi :…

In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are {\em homogeneous} with respect to the action of the M\"{o}bius group consisting of bi-holomorphic automorphisms of the unit…

Let M\"ob be the biholomorphic automorphism group of the unit disc of the complex plane, $\mathcal{H}$ be a complex separable Hilbert space and $\mathcal{U}(\mathcal{H})$ be the group of all unitary operators. Suppose $\mathcal{H}$ is a…