For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference operators acting on functions on the type A weight space. According to the fundamental relation RLL = LLR, the trace of the L-operator gives a commuting difference operators. We show that for the above mentioned L-operator this approach gives Macdonald type operators with elliptic theta function coefficie...

We describe the convex set of the eigenvalues of hermitian matrices which are majorized by sum of m hermitian matrices with prescribed eigenvalues. We extend our characterization to selfadjoint nonnegative (definite) compact operators on a separable Hilbert space. We give necessary and sufficient conditions on the eigenvalue sequence of a selfadjoint nonnegative compact operator of trace class ...

We introduce a new approach for the study of Problem Iterates using theory on general ultradifferentiable structures developed in last years. Our framework generalizes many previous settings including Gevrey case and enables us, first time, to prove non-analytic Theorems non-elliptic differential operators. In particular, by generalizing Theorem Baouendi Metivier we obtain analytic hypoelliptic...

In this paper, some properties of pseudo-differential operators, SG-elliptic partial differential equations with polynomial coefficients and localization operators on space S ν (R), are studied by using fractional Fourier transform. AMS Mathematics Subject Classification (2010): 35S05, 46F12, 47G30.

For differential operators which are invariant under the action of an abelian group Bloch theory is the preferred tool to analyze spectral properties. By shedding some new non-commutative light on this we motivate the introduction of a non-commutative Bloch theory for elliptic operators on Hilbert C-modules. It relates properties of C-algebras to spectral properties of module operators such as ...

Many extensions of Implicit Function Theorem have been proposed for studying non linear differential equations and systems as the already classic Hildebrandt and Graves Theorem [7]. The global invertibility problem has been considered in several forms (see for example [2]), and the differentiability hypothesis has been weakened in various ways to face up different problems connected with differ...

We characterize the essentially normal composition operators induced on the Hardy space H2 by linear fractional maps; they are either compact, normal, or (the nontrivial case) induced by parabolic non-automorphisms. These parabolic maps induce the first known examples of nontrivially essentially normal composition operators. In addition we characterize those linearfractionally induced compositi...