Related papers: A remark on Berezin's quantization and cut locus
We study Berezin-Toeplitz quantization of complex projective spaces $\mathbb{CP}^{d-1}$ and obtain full asymptotic expansions of the Berezin transformation and of products of Toeplitz operators. In each case, the remainder is controlled by…
We study regularization of matrices in the covariant derivative interpretation of matrix models, a typical example of which is the type IIB matrix model. The covariant derivative interpretation provides a possible way in which curved…
We obtain a criterion on the commutativity of polynomials in the enveloping algebra of a Lie algebra in terms of an involution condition with respect to the Berezin bracket. As an application, it is shown that the commutativity requirement…
Looking for a quantum-mechanical implementation of duality, we formulate a relation between coherent states and complex-differentiable structures on classical phase space ${\cal C}$. A necessary and sufficient condition for the existence of…
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…
We extend former results for coherent states on the circle in the literature in two ways. On the one hand, we show that expectation values of fractional powers of momentum operators can be computed exactly analytically by means of Kummer's…
Coherent state operators (CSO) are defined as operator valued functions on G=SL(n,C), homogeneous with respect to right multiplication by lower triangular matrices. They act on a model space containing all holomorphic finite dimensional…
We investigate relations between symmetrizations of quasi-Banach function spaces and constructions such as Calderon-Lozanovskii spaces, pointwise product spaces and pointwise multipliers. We show that under reasonable assumptions the…
In this paper, we study weighted composition operators on Bergman spaces of analytic functions which are square integrable on polydisk. We develop the study in full generality, meaning that the corresponding weighted composition operators…
We give an expression for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charge at inverse temperature {\beta} = 1 (restricted to the line in the presence of a neutralizing field)…
A new characterization of harmonic functions is obtained. It is based on quadrature identities involving mean values over annular domains and over concentric spheres lying within these domains or on their boundaries. The analogous result…
For homogeneous simply connected Hodge manifolds it is proved that the set of coherent vectors orthogonal to a given one is the divisor responsible for the homogeneous holomorphic line bundle of the coherent vectors. In particular, for…
In this paper we construct manifestly covariant relativistic coherent states on the entire complex plane which reproduce others previously introduced on a given $SL(2,R)$ representation, once a change of variables $z\in C\rightarrow z_D \in…
In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.
We describe the local and global structure of the fixed locus for the action of a rational function on the Berkovich projective line over a complete nontrivially-valued algebraically closed nonarchimedean field. This includes a bound for…
We provide a result on the coherent states decomposition for functions in $L^2 (\Bbb T^n)$ where $\Bbb T^n := (\Bbb R / 2\pi \Bbb Z)^n$. Suddenly, we study such a decomposition with respect to the quantum dynamics related to semiclassical…
We establish a quantisation of corner-degenerate symbols, here called Mellin-edge quantisation, on a manifold $M$ with second order singularities. The typical ingredients come from the "most singular" stratum of $M$ which is a second order…
The domain of application of quantization methods is traditionally restricted to smooth classical observables. We show that the coherent states or "anti-Wick" quantization enables us to construct fairly reasonable quantum versions of…
Bifractional transformations which lead to quantities that interpolate between other known quantities, are considered. They do not form a group, and groupoids are used to described their mathematical structure. Bifractional coherent states…
The linearized Boltzmann collision operator has a central role in many important applications of the Boltzmann equation. Recently some important classical properties of the linearized collision operator for monatomic single species were…