Related papers: On the spectra of fermionic second quantization op…
The Goodwillie derivatives of the identity functor on pointed spaces form an operad in spectra. Adapting a definition of Behrens, we introduce mod 2 homology operations for algebras over this operad and prove these operations account for…
Following the definitions of the algebras of differential operators, $\beta$-differential operators, and the quantum differential operators on a noncommutative (graded) algebra given in \cite{LR}, we describe these operators on the free…
This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the…
In the paper we give the results about the spectra of non-invertible weighted composition operators induced by automorphisms on several Hilbert spaces, such as Hardy-Hilbert space $H^2(\mathbb{D})$ and weighted Bergman spaces…
A catalogue of explicit realizations of representations of (super) Lie algebras and quantum algebras in Fock space is presented.
Tensor operators for the Jordanian quantum algebra Uh(sl(2)) are considered. Some explicit examples of them, which are obtained in the boson or fermion realization, are given and their properties are studied. It is also shown that the…
We compute the asymptotic for the eigenvalues of a particular class of compact operators deeply linked with the second variation of optimal control problems. We characterize this family in terms of a set of finite dimensional data and we…
Harmonic oscillator in Fock space is defined. Isospectral as well as polynomiality-of-eigenfunctions preserving, translation-invariant discretization of the harmonic oscillator is presented. Dilatation-invariant and…
In this paper, we establish an a priori second-order estimate for admissible solutions satisfying a dynamic plurisubharmonic condition to equations involving sums of Hessian operators on compact Hermitian manifolds. The estimate is derived…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…
Spectrum of a certain class of first order conformally invariant operators on the sphere is explicitly computed. The class contains the (elliptic verions of) Rarita-Schwinger operator and its higher spin analogues.
In this paper, we give the necessary and sufficient conditions for the boundedness of fractional integral operators on the modulation spaces.
We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the…
Fermion functional integrals are calculated for the Dirac operator of a finite real spectral triple. Complex, real and chiral functional integrals are considered for each KO-dimension where they are non-trivial, and phase ambiguities in the…
Over the past decade classical optical systems with gain or loss, modelled by non-Hermitian parity-time symmetric Hamiltonians, have been deeply investigated. Yet, their applicability to the quantum domain with number-resolved photonic…
Explicit expressions for most interesting quantum operators in optical tomography representation are found. General formalism of symbols of operators is presented in optical tomographic representation. The symbols of the operators are found…
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…
The confluent second-order supersymmetric quantum mechanics, in which the factorization energies tend to a common value, is used to generate Hamiltonians with known spectra departing from the hyperbolic Rosen-Morse and Eckart potentials.…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…