It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters (system functions) and scale filters (multiplication operators in the scale domain), subject to the convergence of the defining integrals. The usual wavelet recons...

Let G be a semisimple Lie group, g its Lie algebra. For any symmetric space M over G we construct a new (deformed) multiplication in the space A of smooth functions on M. This multiplication is invariant under the action of the Drinfeld–Jimbo quantum group U h g and is commutative with respect to an involutive operator˜S : A⊗A → A⊗A. Such a multiplication is unique. Let M be a kählerian symmetr...

In the present paper we study a relation between the Lorentzian twistor equation and CR-geometry. Besides the Dirac operator there is a second important conformally covariant differential operator acting on the spinor fields Γ(S) of a smooth semiRiemannian spin manifold (M,g) of dimension n and index k, the so-called twistor operator D. The twistor operator is defined as the composition of the ...

A multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on L spaces of functions are never compact and then such approximations cannot converge in the norm topology. Instead, we consider how well the spectra of the finite sections approximate the spectrum of the multiplication o...

We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C × C → C. This space of bilinear maps includes the matrix multiplication operator M2 for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix ...

We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C × C → C. This space of bilinear maps includes the matrix multiplication operator M2 for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix ...

Let L be the space of complex-valued functions f on the set of vertices T of an infinite tree rooted at o such that the difference of the values of f at neighboring vertices remains bounded throughout the tree, and let Lw be the set of functions f ∈ L such that |f v − f v− | O |v|−1 , where |v| is the distance between o and v and v− is the neighbor of v closest to o. In this paper, we character...

In this paper we study weighted composition operators on Orlicz spaces. Introduction : Let X and Y be two non empty sets and let F(X) and F(Y) be denoted the topological vector spaces of complex valued functions on X and Y respectively. If T : Y → X is a mapping such that f oT ∈ F (Y) whenever f ∈ F (X), then we can define a composition transformation C T : F (X) → F (Y) by C T f = f oT for eve...

Let D be a bounded symmetric domain in C and let ψ be a complex-valued holomorphic function on D. In this work, we determine the operator norm of the bounded multiplication operator with symbol ψ from the space of bounded holomorphic functions on D to the Bloch space of D when ψ fixes the origin. If no restriction is imposed on the symbol ψ, we have a formula for the operator norm when D is the...