Abstract We study the minimization of a spectral functional made as sum first eigenvalue Dirichlet Laplacian and relative strength Riesz-type interaction functional. show that when Riesz repulsion is below critical value, existence minimizers occurs. Then we prove, by means an expansion analysis, ball rigid minimizer small enough. Eventually for certain regimes repulsion, regular do not exist.

The aim of this work is to introduce a novel concept, Riesz–Dunkl fractional derivatives, within the context Dunkl-type operators. A particularly noteworthy revelation that when specific parameter κ equals zero, derivative smoothly reduces both well-known Riesz and second-order derivative. Furthermore, we new concept: Sobolev space. This space defined characterized using versatile framework Dun...

In this note we present a review, some considerations and new results about maps with values in distribution space domain σ-finite measure X. Namely, is survey Bessel maps, frames bases (in particular Riesz Gel’fand bases) space. setting, the Riesz-Fischer semi-frames are defined them obtained. Some examples tempered distributions examined.

It is shown that product BMO of S.-Y.A.Chang and R. Fefferman, defined on the space R1 ⊗ · · ·⊗Rdt , can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of R. Coifman, R. Rochberg, and G. Weiss [8], and at the same time extends the work of M. Lacey and S. Ferguson [12] and M. Lacey and E. Terwilleger [19], on multiparameter c...

Stein’s higher Riesz transforms are translation invariant operators on L2(Rn) built from multipliers whose restrictions to the unit sphere are eigenfunctions of the Laplace–Beltrami operators. In this article, generalizing Stein’s higher Riesz transforms, we construct a family of translation invariant operators by using discrete series representations for hyperboloids associated to the indefini...

In this paper we study systems in which the system operator, A, has a Riesz basis of (generalized) eigenvectors. We show that this class is subset of the class of spectral operators as studied by Dunford and Schwartz. For these systems we investigate several system theoretic properties, like stability and controllability. We apply our theory to Euler-Bernoulli beam with structural damping.