Related papers: Cordes characterization for pseudodifferential ope…

Given a Lie group $G$, a compact subgroup $K$ and a representation $\tau\in\hat K$, we assume that the algebra of $\text{End}(V_\tau)$-valued, bi-$\tau$-equivariant, integrable functions on $G$ is commutative. We present the basic facts of…

We present a conjecture (and a proof for G=SL(2)) generalizing a result of J. Arthur which expresses a character value of a cuspidal representation of a $p$-adic group as a weighted orbital integral of its matrix coefficient. It also…

We investigate the space $X$ of unitary hermitian matrices over $\frp$-adic fields through spherical functions. First we consider Cartan decomposition of $X$, and give precise representatives for fields with odd residual characteristic,…

First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield of pseudodifferential operators over K by the subalgebra of all differential operators. Second, we show that…

Let $E$ and $P$ be subsets of a Banach space $X$, and let us define the unit sphere around $E$ in $P$ as the set $$Sph(E;P) :=\left\{ x\in P : \|x-b\|=1 \hbox{ for all } b\in E \right\}.$$ Given a C$^*$-algebra $A$, and a subset $E\subset…

Given a positive operator-valued measure $\nu$ acting on the Borel sets of a locally compact Hausdorff space $X$, with outcomes in the algebra $\mathcal B(\mathcal H)$ of all bounded operators on a (possibly infinite-dimensional) Hilbert…

Let $H$ be an infinite dimensional separable Hilbert space, $B(H)$ the $C^*$-algebra of all bounded linear operators on $H,$ $U(B(H))$ the unitary group of $B(H)$ and ${\cal K}\subset B(H)$ the ideal of compact operators. Let $G$ be a…

Cordes' characterization of Heisenberg-smooth operators bridges a gap between the theory of pseudo-differential operators and quantum harmonic analysis (QHA). We give a new proof of the result by using the phase space formalism of QHA. Our…

For a large class of semiclassical pseudodifferential operators, including Schr\"odinger operators, $ P (h) = -h^2 \Delta_g + V (x) $, on compact Riemannian manifolds, we give logarithmic lower bounds on the mass of eigenfunctions outside…

A Hilbert space operator $U$ is called universal (in the sense of Rota) if every Hilbert space operator is similar to a multiple of $U$ restricted to one of its invariant subspaces. It follows that the Invariant Subspace Problem for Hilbert…

Let $\mathcal{B} (X)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space $X$. For an operator $ T \in \mathcal{B} (X)$, $K(T)$ denotes as usual the analytic core of $T$. We determine the form of…

Let B be a unital C*-subalgebra of a unital C*-algebra A, so that A/B is an abstract operator space. We show how to realize A/B as a concrete operator space by means of a completely contractive map from A into the algebra of operators on a…

Let $A$ be a real commutative Banach algebra with unity. Let $a_0\in A\setminus\{0\}$. Let $\mathbb Z a_0:=\{na_0\}_{n\in \mathbb Z}$. Then, $\mathbb Z a_0$ is a discrete subgroup of $A$. For any $n\in \mathbb Z$, the Frechet derivative of…

Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…

It is proved that a commutative algebra $A$ of operators on a reflexive real Banach space has an invariant subspace if each operator $T\in A$ satisfies the condition $$\|1- \varepsilon T^2\|_e \le 1 + o(\varepsilon) \text{ when }…

We investigate the spectral and index-theoretic properties of the Hodge-Dirac operator $D = \mathrm{d} + \mathrm{d}^*$ acting on the Banach space $\mathrm{L}^p(\Omega^\bullet(M))$ of differential forms over a compact Riemannian manifold…

Polyhomogeneous symbols, defined by Kohn-Nirenberg and H\"ormander in the 60's, play a central role in the symbolic calculus of most pseudodifferential calculi. We prove a simple characterisation of polyhomogeneous functions which avoids…

The smooth hermitian representations of a split reductive p-adic group whose restriction to a maximal hyperspecial compact subgroup contain a single K-type with Iwahori fixed vectors have been studied in [D. Barbasch, A. Moy, Classification…

In this paper, we study harmonic analysis on the affine Poincar\'e group $\mathcal{P}_{aff}$, which is a non-unimodular group, and obtain pseudo-differential operators with operator valued symbols. More precisely, we study the boundedness…

Let G be a locally compact group, A(G) its Fourier algebra and L1(G) the space of Haar integrable functions on G. We study the Segal algebra SA(G)=A(G)\cap L1(G) in A(G). It admits an operator space structure which makes it a completely…