Generalized Scalar Operators as Dilations

Generalized Scalar Operators as Dilations

It is shown that polynomially bounded operators on Banach spaces have polynomially bounded dilations which have spectrum in the unit circle and are generalized scalar. The proof also yields a description of all compressions of generalized scalar operators with spectrum in the unit circle.

Generalized Continuous Frames for Operators

In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ wi...

Generalized Stable Multivariate Distribution and Anisotropic Dilations

After having closely re-examined the notion of a Lévy’s stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with the help of non isotropic dilations and a related notion of generalized scale. In this framework, the components of a stable vector may not only have distinct ...

1 Simple Wavelet Sets for Scalar Dilations in R 2

Hill Operators and Spectral Operators of Scalar

We derive necessary and sufficient conditions for a one-dimensional periodic Schrödinger (i.e., Hill) operator H = −d 2 /dx 2 + V in L 2 (R) to be a spectral operator of scalar type. The conditions demonstrate the remarkable fact that the property of a Hill operator being a spectral operator is independent of smoothness (or even analyticity) properties of the potential V. R ´ ESUMÉ. Quand un op...