In a variety of situations, integrals of products of eigenfunctions have faster decay than smoothness entails. This phenomenon does not appear for abelian or compact groups, since irreducibles are finite-dimensional, so the decomposition of a tensor product of irreducibles is finite. In contrast, for non-compact, nonabelian groups irreducibles are typically infinite-dimensional, and the decompo...

We show that if a holomorphic Hamiltonian system is holomorphically integrable in the non-commutative sense in a neighbourhood of a non-equilibrium phase curve which is located at a regular level of the first integrals, then the identity component of the differential Galois group of the variational equations along the phase curve is Abelian. Thus necessary conditions for the commutative and non...

In this article we introduce algorithms which compute iterations of Gauss-Manin connections, Picard-Fuchs equations of Abelian integrals and mixed Hodge structure of affine varieties of dimension n in terms of differential forms. In the case n = 1 such computations have many applications in differential equations and counting their limit cycles. For n > 3, these computations give us an explicit...

In this talk the relation between the semiclassical approach and the concept of diffractive parton densities is discussed. The proton rest frame calculation is organized in a way that exhibits the hard partonic cross section and the diffractive parton density as the two fundamental ingredients. The latter one is a non-perturbative quantity which, in the present model, is explicitly given by int...

We construct the classical W -algebras for some non-abelian Toda systems associated with the Lie groups GL 2n(R) and Spn(R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian counterparts. The convenient block matrix representaion for the Toda equations is used. The infinitesimal symmetry transformations generated by the elements o...

We construct the classical W -algebras for some non-abelian Toda systems associated with the Lie groups GL 2n(R) and Spn(R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian counterparts. The convenient block matrix representation for the Toda equations is used. The infinitesimal symmetry transformations generated by the elements ...

We construct the classical W -algebras for some non-abelian Toda systems associated with the Lie groups GL 2n(R) and Spn(R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian counterparts. The convenient block matrix representaion for the Toda equations is used. The infinitesimal symmetry transformations generated by the elements o...

A subset of an abelian semigroup is called an asymptotic basis for the semigroup if every element of the semigroup with at most finitely many exceptions can be represented as the sum of two distinct elements of the basis. The representation function of the basis counts the number of representations of an element of the semigroup as the sum of two distinct elements of the basis. Suppose there is...

Abstract We construct a large family of Fourier interpolation bases for functions analytic in strip symmetric about the real line. Interesting examples involve nontrivial zeros Riemann zeta function and other L -functions. establish duality principle terms certain kernels general Dirichlet series with variable coefficients. Such admit meromorphic continuation, poles at sequence dual to frequenc...