We present an approach to Hida’s theory of p-adically interpolating the ordinary cohomology of arithmetic groups and we discuss some application of this approach to special values of L-functions. Mathematics Subject Classification (2010). 11F75, 11F33, 11F67.

We work out the effective scaling approach to frictionless quantum quenches in a one-dimensional Bose gas trapped harmonic trap. The produces an auxiliary equation for parameter interpolating between noninteracting and Thomas-Fermi limits. This allows us implement quench by inversely engineering smooth trap frequency, as compared two-jump bang control. Our result is beneficial design shortcut-t...

In this paper, by means of a new recursive algorithm of non-tensor-producttyped divided differences, bivariate polynomial interpolation schemes are constructed over nonrectangular meshes firstly, which is converted into the study of scattered data interpolation. And the schemes are different as the number of scattered data is odd and even, respectively. Secondly, the corresponding error estimat...

Free interpolation in Hardy spaces is characterized by the well-known Carleson condition. The result extends to Hardy-Orlicz spaces contained in the scale of classical Hardy spaces H, p > 0. For the Smirnov and the Nevanlinna classes, interpolating sequences have been characterized in a recent paper in terms of the existence of harmonic majorants (quasi-bounded in the case of the Smirnov class)...

In this paper, we present a numerical method for solving Hallen’s integral equation based on radial basis functions (RBFs). This method will represent the solution of Hallen’s integral equation by interpolating the radial basis functions based on Legendre-Gauss-Lobatto(LGL) nodes and weights. The numerical results show that the proposed method for Hallen’s integral equation is very accurate and...

We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of interpolating and sampling sequences for this space. We also give a description of the trace of such functions to sequences of critical density in terms of a cancellation condition.

Green’s functions are gauge-dependent quantities. Thus, the manifestation of confinement in these correlation functions also depends on the gauge. Here we use lattice gauge theory to study the gluon and the ghost propagators in a gauge (the so-called λ -gauge) interpolating between the Landau and the Coulomb gauge. Results are compared to the usual minimal Landau gauge.

For a family of weight functions that include the general Jacobi weight functions as special cases, exact condition for the convergence of the Fourier orthogonal series in the weighted L space is given. The result is then used to establish a Marcinkiewicz-Zygmund type inequality and to study weighted mean convergence of various interpolating polynomials based on the zeros of the corresponding o...