Related papers: Quantum cutting and a Szeg\"o limit theorem
We formulate a variant of Fourier restriction for operators in Schatten classes, where the Fourier-Wigner transform of a bounded operator replaces the Fourier transform of a function. The Fourier-Wigner transform is closely related to the…
In this paper, we develop a semi-classical analysis on H-type groups. We define semi-classical pseudodifferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we…
Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and…
We derive an explicit formula for the general solution of the cubic Szeg\"o equation and of the evolution equation of the corresponding hierarchy. As an application, we prove that all the solutions corresponding to finite rank Hankel…
We define and study dense Frechet subalgebras of compact quantum groups consisting of elements rapidly decreasing with respect to an unbounded sequence of real numbers. Further, this sequence can be viewed as the eigenvalues of a Dirac-like…
The volume operator plays a pivotal role for the quantum dynamics of Loop Quantum Gravity (LQG), both in the full theory and in truncated models adapted to cosmological situations coined Loop Quantum Cosmology (LQC). It is therefore crucial…
By using a ``quantum-to-classical" reduction formula on the Gromov-Witten invariants of flag vaireities $F\ell_n$, we provide a new proof of the Seidel operator on the quantum cohomology ring $QH^*(F\ell_n)$. Further, we reprove a quantum…
A framework to describe a broad class of physical operations (including unitary transformations, dissipation, noise, and measurement) in a quantum optics experiment is given. This framework provides a powerful tool for assessing the…
Application of the fractional calculus to quantum processes is presented. In particular, the quantum dynamics is considered in the framework of the fractional time Schr\"odinger equation (SE), which differs from the standard SE by the…
We introduce a simplified (coarse) version of pseudo-differential calculus for operators of order zero on complete Riemannian manifolds. This calculus works for the usual Hormander (1,0) class of operators, as well as for…
Truncated Toeplitz operators are compressions of multiplication operators on $L^2$ to model spaces (that is, subspaces of $H^2$ which are invariant with respect to the backward shift). For this class of operators we prove certain Szeg\"o…
We define the full and reduced non-self-adjoint operator algebras associated with \'etale categories and restriction semigroups, answering a question posed by Kudryavtseva and Lawson in \cite{lawson}. Moreover, we define the semicrossed…
The generalized h-dependent operator algebra is defined ($0\leq h \leq h_o$). For h= h_o it becomes equivalent to the quantum mechanical algebra of observables and for h=0 it is equivalent to the classical one. We show this by proposing how…
We extend the well-known Katznelson-Tzafriri theorem, originally posed for power-bounded operators, to the case of Ces\`aro bounded operators of any order $\alpha>0.$ For this purpose, we use a functional calculus between a new class of…
We derive a semi-classical nonequilibrium work identity by applying the Wigner-Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us, to the leading order in $\hbar$, to overcome the problem of…
Motivated by generalizing Szemer\'edi's theorem, we the elements in a discrete quantum group fixing a sequence of finite subsets and prove that the set of these elements is a quantum subgroup. Using this we obtain a version of mean ergodic…
We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
This paper outlines a covariant theory of operators defined on groups and homogeneous spaces. A systematic use of groups and their representations allows to obtain results of algebraic and analytical nature. The consideration is…
In this paper, we study Toeplitz operators on generalized flag manifolds of compact Lie groups using a representation-theoretic point of view. We prove several basic properties of these Toeplitz operators, including an abstract formula for…