Related papers: C*-Algebra-valued-symbol pseudodifferential operat…

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of…

Let H_c be the rational Cherednik algebra of type A_{n-1} with spherical subalgebra U_c = eH_ce. Then U_c is filtered by order of differential operators, with associated graded ring gr U_c = C[h+h*]^W, where W is the n-th symmetric group.…

We define a second-order differential operator $\hat{C}$ on the Hilbert space $L^2([-v_c, v_c])$, constructed from a smooth deformation function $C(v)$. The operator is considered on the Sobolev domain $H^2([-v_c, v_c]) \cap H^1_0([-v_c,…

In this paper, we define in an intrinsic way operators on a compact Lie group by means of symbols using the representations of the group. The main purpose is to show that these operators form a symbolic pseudo-differential calculus which…

We describe certain $C^*$-algebras generated by Toeplitz operators with nilpotent symbols and acting on a poly-Bergman type space of the Siegel domain $D_{2} \subset \mathbb{C}^{2}$. Bounded measurable functions of the form $c(\text{Im}\,…

Investigating the direct integral decomposition of von Neumann algebras of bounded module operators on self-dual Hilbert W*-moduli an equivalence principle is obtained which connects the theory of direct disintegration of von Neumann…

Let $G$ be a locally compact abelian Hausdorff topological group which is non-compact and whose Pontryagin dual $\Gamma$ is partially ordered. Let $\Gamma^{+}\subset\Gamma$ be the semigroup of positive elements in $\Gamma$. The Hardy space…

We define new symbol classes for pseudodifferntial operators and investigate their pseudodifferential calculus. The symbol classes are parametrized by commutative convolution algebras. To every solid convolution algebra over a lattice we…

Iteration of a rational function $R$ gives a complex dynamical system on the Riemann sphere. We introduce a $C^*$-algebra ${\mathcal O}_R$ associated with $R$ as a Cuntz-Pimsner algebra of a Hilbert bimodule over the algebra $A = C(J_R)$ of…

A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of…

Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…

Let us consider, for $n \geq 3$, the Cartan domain $\mathrm{D}_n^{\mathrm{IV}}$ of type IV. On the weighted Bergman spaces $\mathcal{A}^2_\lambda(\mathrm{D}_n^{\mathrm{IV}})$ we study the problem of the existence of commutative…

For a symplectic manifold admitting a metaplectic structure and for a Kuiper map, we construct a complex of differential operators acting on exterior differential forms with values in the dual of the Kostant's symplectic spinor bundle.…

Let G be a discrete group and $\Gamma$ an almost normal subgroup. The operation of cosets concatanation extended by linearity gives rise to an operator system that is embeddable in a natural C* algebra. The Hecke algebra naturally embeds as…

We study Toeplitz operators on Hilbert spaces of holomorphic functions on symmetric domains, and more generally on certain algebraic subvarieties, determined by integration over boundary orbits of the underlying domain. The main result…

The algebra $\Psi(M)$ of order zero pseudodifferential operators on a compact manifold $M$ defines a well-known $C^*$-extension of the algebra $C(S^*M)$ of continuous functions on the cospherical bundle $S^*M\subset T^*M$ by the algebra…

An operator *-algebra is a non-selfadjoint operator algebra with completely isometric involution. We show that any operator *-algebra admits a faithful representation on a Hilbert space in such a way that the involution coincides with the…

The purpose of this paper is to introduce new definitions of H\"ormander classes for pseudo-differential operators over the compact group of $p$-adic integers. Our definitions possess a symbolic calculus, asymptotic expansions and…

Boutet de Monvel's calculus provides a pseudodifferential framework which encompasses the classical differential boundary value problems. In an extension of the concept of Lopatinski and Shapiro, it associates to each operator two symbols:…

The classical radial part formula for the invariant differential operators and the K-invariant functions on a Riemannian symmetric space G/K is generalized to some non-invariant cases by use of Cherednik operators and a graded Hecke algebra…