Hidden symmetry from supersymmetry in one-dimensional quantum mechanics.
The aim of this paper is to extend the study of Riesz transforms associated to Dunkl Ornstein-Uhlenbeck operator considered by A. Nowak, L. Roncal and K. Stempak to higher order.
In this article, we shall extend the formalization of [10] to discuss higher-order partial differentiation of real valued functions. The linearity of this operator is also proved (refer to [10], [12] and [13] for partial differentiation).
In this paper we consider a class of Hankel operators with operator valued symbols on the Hardy space where is a separable infinite dimensional Hilbert space and showed that these operators are unitarily equivalent to a class of integral operators in We then obtained a generalization of Hilbert inequality for vector valued functions. In the continuous case the corresponding integral operator has matrix valued kernels and in the discrete case the sum involves inner product of vectors in the...
It is an open question whether every Fourier type 2 operator factors through a Hilbert space. We show that at least the natural gradations of Fourier type 2 norms and Hilbert space factorization norms are not uniformly equivalent. A corresponding result is also obtained for a number of other sequences of ideal norms instead of the Fourier type 2 gradation including the Walsh function analogue of Fourier type. Our main tools are ideal norms and random matrices.
The irreducible Hilbert space representations of a ⁎-algebra, the graded analogue of the Lie algebra of the group of plane motions, are classified up to unitary equivalence.
In this paper, several sufficient conditions for boundedness of the Hilbert transform between two weighted Lp-spaces are obtained. Invariant A∞ weights are obtained. Several characterizations of invariant A∞ weights are given. We also obtain some sufficient conditions for products of two Toeplitz operators of Hankel operators to be bounded on the Hardy space of the unit circle using Orlicz spaces and Lorentz spaces.
On complete pseudoconvex Reinhardt domains in , we show that there is no nonzero Hankel operator with anti-holomorphic symbol that is Hilbert-Schmidt. In the proof, we explicitly use the pseudoconvexity property of the domain. We also present two examples of unbounded non-pseudoconvex domains in that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols. In the first example the Bergman space is finite dimensional. However, in the second example the Bergman space is infinite...