相关论文: Symbolic calculus on the time-frequency half-plane
We develop a singular pseudodifferential calculus. The symbols that we consider do not satisfy the standard decay with respect to the frequency variables. We thus adopt a strategy based on the Calderon-Vaillancourt Theorem. The remainders…
We set up a left ring of fractions over a certain ring of boundary problems for linear ordinary differential equations. The fraction ring acts naturally on a new module of generalized functions. The latter includes an isomorphic copy of the…
We introduce a symbolic operator framework for simulating quantum photonic systems that works directly with the canonical commutation relations and the Weyl algebra. Unlike existing Fock-space or Gaussian simulators, our method treats…
A time-frequency diagram is a commonly used visualization for observing the time-frequency distribution of radio signals and analyzing their time-varying patterns of communication states in radio monitoring and management. While it excels…
The purpose of this note is to compare the properties of the symbolic pseudo-differential calculus on the Heisenberg and on the Engel groups; nilpotent Lie groups of 2-step and 3-step, respectively. Here we provide a preliminary analysis of…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
We are consider domains in cotangent bundles with the property that the null foliation of their boundary is fibrating and the leaves satisfy a Bohr-Sommerfeld condition (for example, the unit disk bundle of a Zoll metric). Given such a…
We introduce a new family of symmetric functions, which are $q$-analogues of products of Schur functions defined in terms of ribbon tableaux. These functions can be interpreted in terms of the Fock space representation of the quantum affine…
We consider bilinear oscillatory integrals, i.e. pseudo-product operators whose symbol involves an oscillating factor. Lebesgue space inequalities are established, which give decay as the oscillation becomes stronger ; this extends the…
We use the functorial properties of Rieffel's pseudodifferential calculus to study families of operators associated to topological dynamical systems acted by a symplectic space. Information about the spectra and the essential spectra are…
Covariant integral quantisation using coherent states for semidirect product groups is studied and applied to the motion of a particle on the circle. In the present case the group is the Euclidean group E$(2)$. We implement the quantisation…
The aim of this work is to derive a symbol calculus on $L^2(\mathbb{R})$ for one-dimensional Hausdorff operators in apparently the most general form.
We revise a monogenic calculus for several non-commuting operators, which is defined through group representations. Instead of an algebraic homomorphism we use group covariance. The related notion of joint spectrum and spectral mapping…
We consider elliptic operators associated with discrete groups of quantized canonical transformations. In order to be able to apply results from algebraic index theory, we define the localized algebraic index of the complete symbol of an…
We study Frobenius-Schur indicators of the regular representations of finite-dimensional semisimple Hopf algebras, especially group-theoretical ones. Those of various Hopf algebras are computed explicitly. In view of our computational…
On the torus, it is possible to assign a global symbol to a pseudodifferential operator using Fourier series. In this paper we investigate the relations between the local and global symbols for the operators in the classical H\"ormander…
We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of…
We introduce the affine Vogan diagrams of complex simple Lie algebras. These are generalizations of Vogan diagrams, and we study the involutions represented by them. We apply these diagrams to study the symmetric pairs, in particular the…
In this article, I introduce a group-theoretical method to prove positivity of certain linear combinations (with coefficients generally lying in $\mathbb{C}$) of exponential functions under a set of semidefinite linear constraints. The…
This paper mainly studies totally Abelian operators in the context of analytic Toeplitz operators on both the Hardy and Bergman space. When the symbol is a meromorphic function on $\mathbb{C}$, we establish the connection between totally…