Related papers: Star product algebras of test functions

For a bivariate $P(x,y) \in \mathbb{R}[x,y]\setminus (\mathbb{R}[x] \cup \mathbb{R}[y])$, our first result shows that for all finite $A \subseteq \mathbb{R}$, $|P(A,A)|\geq \alpha|A|^{5/4}$ with $\alpha =\alpha(\mathrm{deg} P) \in…

We describe several infinite series of rational conformal field theories whose conformal characters are modular units, i.e. which are modular functions having no zeros or poles in the upper complex half plane, and which thus possess simple…

A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with…

Let $S$ be a discrete abelian semigroup with unit and concellations and $\widehat {S}$ the semigroup of semicharacters of $S$. We shaw that the strong boundary and the Shilov boundary of the algebra of generalized analytic functions defined…

The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the…

$C^*$-algebras, group algebras, and the algebra $\mathcal{A}(X)$ of approximable operators on a Banach space $X$ having the bounded approximation property are known to be zero product determined. We are interested in giving a quantitative…

Let $f$ and $g$ be functions, not identically zero, in the Fock space $F^2$ of $C_n$. We show that the product $T_fT_{\bar g}$ of Toeplitz operators on $F^2$ is bounded if and only if $f(z)=e^{q(z)}$ and $g(z)=ce^{-q(z)}$, where $c$ is a…

We prove that if $X = X_1 \times \dots \times X_n$ is a product of hyperbolic Riemann surfaces of finite type and $Y = \Omega/\Gamma$ is a complex manifold, where $\Omega$ is a bounded simply-connected domain in $\mathbb{C}^m$, then the…

We show that a projective space P^\infty(Z/2) endowed with the Alexandrov topology is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over…

Motivated by the Schwartz space of tempered distributions $\mathscr S^\prime$ and the Kondratiev space of stochastic distributions $\mathcal S_{-1}$ we define a wide family of nuclear spaces which are increasing unions of (duals of) Hilbert…

We calculate the stable pair theory of a projective surface $S$. For fixed curve class $\beta\in H^2(S)$ the results are entirely topological, depending on $\beta^2$, $\beta.c_1(S)$, $c_1(S)^2$, $c_2(S)$, $b_1(S)$ \emph{and} invariants of…

This is the final version of my master thesis. I prove that there are no twist star products on the 2-sphere and on the higher genus pretzel surfaces deforming a symplectic structure. One of the key arguments is that a connected compact…

In this paper we explicitly construct local $\nu$-Euler derivations $\mathsf E_\alpha = \nu \partial_\nu + \Lie{\xi_\alpha} + \mathsf D_\alpha$, where the $\xi_\alpha$ are local, conformally symplectic vector fields and the $\mathsf…

This is an expository note on Fedosov's construction of deformation quantization. Given a symplectic manifold and a connection on it, we show how to calculate the star-product step by step. We draw simple diagrams to solve the recursive…

In this paper, we investigate properties of Gelfand-Tsetlin bases mainly for spherical monogenics, that is, for spinor valued or Clifford algebra valued homogeneous solutions of the Dirac equation in the Euclidean space. Recently it has…

Let $A$ be a right noetherian algebra over a field $k$. If the base field extension $A \otimes_k K$ remains right noetherian for all extension fields $K$ of $k$, then $A$ is called stably right noetherian over $k$. We develop an inductive…

We construct a Frechet space as a subspace of C^\omega(C^n) where the Wick star product converges and is continuous. The resulting Frechet algebra A_h is studied in detail including a *-representation of A_h in the Bargmann-Fock space and a…

A topological space satisfies $\GNga$ (also known as Gerlits--Nagy's property $\gamma$) if every open cover of the space such that each finite subset of the space is contained in a member of the cover, contains a point-cofinite cover of the…

We prove an algebra property under pointwise multiplication for Besov spaces defined on Lie groups of polynomial growth. When the setting is restricted to the case of H-type groups, this algebra property is generalized to paraproduct…

It is investigated necessary and sufficient conditions on topological spaces $X=\prod\limits _{s\in S}X_s$ and $Y=\prod\limits _{t\in T}Y_t$ for the dependence of every separately continuous functions $f:X\times Y\to \mathbb R$ on at most…