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BILINEAR PSEUDODIFFERENTIAL OPERATORS ON MODULATION SPACES
Bilinear operators Gabor frames modulation spaces moderate weights pseudodifferential operators sequence spaces short-time Fourier transform time-frequency analysis weighted spaces
2015/12/10
We use the theory of Gabor frames to prove the boundedness of bilinear pseudodifferentialoperators on products of modulation spaces. In particular,we show that bilinear pseudodifferential operators co...
BOUNDEDNESS OF MULTILINEAR PSEUDO-DIFFERENTIAL OPERATORS ON MODULATION SPACES
MULTILINEAR PSEUDO-DIFFERENTIAL OPERATORS MODULATION SPACES
2015/12/10
Boundedness results for multilinear pseudodifferential operators on products of modulation spaces are derived based on ordered integrability conditions on the short-time Fourier transform of the opera...
CASIMIR OPERATORS AND MONODROMY REPRESENTATIONS OF GENERALISED BRAID GROUPS
CASIMIR OPERATORS MONODROMY REPRESENTATIONS GENERALISED BRAID GROUPS
2015/10/14
Let g be a complex, simple Lie algebra with Cartan subalgebra h and Weyl group W . We construct a one parameter family of flat connections ∇κ on h with values in any finite–dimensional g–moduleV...
THE NONCOMMUTATIVE WIENER LEMMA,LINEAR INDEPENDENCE,AND SPECTRAL PROPERTIES OF THE ALGEBRA OF TIME-FREQUENCY SHIFT OPERATORS
NONCOMMUTATIVE WIENER LEMMA LINEAR INDEPENDENCE SPECTRAL PROPERTIES OF THE ALGEBRA TIME-FREQUENCY SHIFT OPERATORS
2015/9/29
In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracia...
A fast algorithm for multilinear operators
Multilinear operators Fast Fourier transform Multiscale decomposition Low-rank approximation
2015/7/14
This paper introduces a fast algorithm for computing multilinear integrals which are defined through Fourier multipliers. The algorithm is based on generating a hierarchical decomposition of the summa...
Restrictions to Invariant Subspaces of Composition Operators on the Hardy Space of the Disk
composition operator hardy semigroup
2015/1/19
Invariant subspaces are a natural topic in linear algebra and operator theory. In some rare cases, the restrictions of operators to different invariant subspaces are unitarily equivalent, such as cert...
Baxter operators for arbitrary spin II
Baxter operators arbitrary spin II High Energy Physics - Theory Quantum Algebra
2011/10/10
Abstract: This paper presents the second part of our study devoted to the construction of Baxter operators for the homogeneous closed XXX spin chain with the quantum space carrying infinite or finite-...
Manin triples and differential operators on quantum groups
Manin triples differential operators quantum groups
2011/1/18
Let (a,m, l) be a Manin triple, and let M, L be algebraic groups with Lie algebras m, l respectively. We point out that the product M×L carries a natural structure of Poisson manifold,whose Poisson te...
The Darboux coordinates for a new family of Hamiltonian operators and linearization of associated evolution equations
Hamiltonian operators bi-Hamiltonian systems evolution equations linearization
2011/1/20
A. de Sole, V. G. Kac, and M. Wakimoto have recently introduced a new family of compatible
Hamiltonian operators of the form H(N,0) = D2 ◦ ((1/u)◦D)2n ◦D, where N = 2n+3, n = 0, 1, ...
Selected results on Lie supergroups and their radial operators
Selected results Lie supergroups radial operators
2011/2/25
Foundational material on complex Lie supergroups and their radial operators is presented. In particular, Berezin’s recursion formula for describing the radial parts of fundamental operators in general...
Modal Hamiltonian interpretation of quantum mechanics and Casimir operators: the road towards quantum field theory
Modal Hamiltonian interpretation of quantum mechanics Casimir operators quantum field theory
2011/3/2
The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) fields.
We give a full set of Casimir operators for the symplectic group of arbitrary genus in terms of a basis chosen such that the action on representations of known $K$-type becomes transparent. We give ex...
Fock Spaces, Landau Operators and the Regular Solutions of time-harmonic Maxwell equations
Fock Spaces Landau Operators time-harmonic Maxwell equations
2010/11/24
We investigate the solution representation for Maxwell equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. This gives a characterization f...
Spatial isomorphisms of algebras of truncated Toeplitz operators
Spatial isomorphisms algebras Toeplitz operators
2010/11/9
We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maxima...
Rank of Projection-Algebraic Representations of Some Differential Operators
Rank of Projection-Algebraic Differential Operators
2010/11/22
The Lie-algebraic method approximates differential operators that are formal polynomials of {1,x,d/dx} by linear operators acting on a finite dimensional space of polynomials. In this paper we prove ...