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Abelian Integrals: From the Tangential 16th Hilbert Problem to the Spherical Pendulum

2016

In this chapter we deal with abelian integrals. They play a key role in the infinitesimal version of the 16th Hilbert problem. Recall that 16th Hilbert problem and its ramifications is one of the principal research subject of Christiane Rousseau and of the first author. We recall briefly the definition and explain the role of abelian integrals in 16th Hilbert problem. We also give a simple well-known proof of a property of abelian integrals. The reason for presenting it here is that it serves as a model for more complicated and more original treatment of abelian integrals in the study of Hamiltonian monodromy of fully integrable systems, which is the main subject of this chapter. We treat i…

Regularity of a Degenerated Convolution Semi-Group Without to Use the Poisson Process

2011

We translate in semi-group theory our regularity result for a degenerated convolution semi-group got by the Malliavin Calculus of Bismut type for Poisson processes.

Polaroid-Type Operators

2018

In this chapter we introduce the classes of polaroid-type operators, i.e., those operators T ∈ L(X) for which the isolated points of the spectrum σ(T) are poles of the resolvent, or the isolated points of the approximate point spectrum σap(T) are left poles of the resolvent. We also consider the class of all hereditarily polaroid operators, i.e., those operators T ∈ L(X) for which all the restrictions to closed invariant subspaces are polaroid. The class of polaroid operators, as well as the class of hereditarily polaroid operators, is very large. We shall see that every generalized scalar operator is hereditarily polaroid, and this implies that many classes of operators acting on Hilbert s…

Commutative Partial O*-Algebras

2002

This chapter is devoted to the integrability of commutative partial O*-algebras. Three notions of weak commutativity, commutativity and strong commutativity of an O*-vector space are defined and investigated. In Section 3.1, we analyze the relation between the integrability of weakly commutative O*-vector space M and the commutativity of the von Neumann algebra (M w ′ )′. In Section 3.2, we study the integrable extensions of partial O*-algebras. In Section 3.3, we describe another explicit example, namely, the partial O*-algebra M[S, T] generated by two weakly commuting symmetric operators S and T defined on a common dense domain in a Hilbert space. In particular, we investigate in detail t…

Isometries between spaces of multiple Dirichlet series

2019

Abstract In this paper we study spaces of multiple Dirichlet series and their properties. We set the ground of the theory of multiple Dirichlet series and define the spaces H ∞ ( C + k ) , k ∈ N , of convergent and bounded multiple Dirichlet series on C + k . We give a representation for these Banach spaces and prove that they are all isometrically isomorphic, independently of the dimension. The analogous result for A ( C + k ) , k ∈ N , which are the spaces of multiple Dirichlet series that are convergent on C + k and define uniformly continuous functions, is obtained.

MQDO theoretical study of the C1Π–X1Σ+ band system of HCl

2008

Abstract Oscillator strengths for P, Q and R rotational lines belonging to the (0, v ″ = 0, 1) and (1, v ″ = 0, 1) bands for the C 1 Π–X 1 Σ + system of HCl have been theoretically studied. The calculations have been performed by following the molecular quantum defect orbital methodology, which has earlier proved to yield accurate intensities for transitions involving Rydberg states in a variety of molecular species. The results appear to be in good accord with the available experimental values. Predictions of a number of unknown intensities have also been made. We expect that the present data might be of help in the interpretation of future experimental measurements.

Deformed Canonical (anti-)commutation relations and non-self-adjoint hamiltonians

2015

Effect of Fe-incorporation on Structural and Optoelectronic Properties of Spin Coated p/n Type ZnO Thin Films

2020

Inheritance in the water frog Rana ridibunda Pallas, 1771 - Is it Mendelian or hemiclonal?

2008

The genome of Rana ridibunda has been detected in all known hybridogenetic water frog systems. This raises the question whether R. ridibunda is pre-adapted to reproduce hemiclonally by hybridogenesis. We allozymatically compared genotypes of primary oocytes and somatic cells of R. ridibunda females from several sites in southern France. In case of hemiclonal reproduction only one allele per locus is expected to be detectable in oocytes. However, patterns detected from oocytes of analysed females were not different from those of sexually reproducing water frogs. We therefore conclude that R. ridibunda in southern France reproduces sexually and is not pre-adapted to hemiclonal reproduction.

Carleson's counterexample and a scale of Lorentz-BMO spaces on the bitorus

2005

We introduce a full scale of Lorentz-BMO spaces BMO L p,q on the bidisk, and show that these spaces do not coincide for different values ofp andq. Our main tool is a detailed analysis of Carleson's construction in [C].