We introduce the sequence of generalized Gončarov polynomials, which is a basis for the solutions to the Gončarov interpolation problem with respect to a delta operator. Explicitly, a generalized Gončarov basis is a sequence (tn(x))n≥0 of polynomials defined by the biorthogonality relation εzi(d (tn(x))) = n!δi,n for all i, n ∈ N, where d is a delta operator, Z = (zi)i≥0 a sequence of scalars, ...

In this paper, we propose and analyze a multiuser receiver using a decorrelating filter and Viterbi decoders for trellis-coded direct-sequence code-division multiple-access (DS/CDMA) systems with biorthogonal signal constellation in asynchronous channels. The biorthogonality is implemented by user signature waveforms and the decorrelating filter. The performance of the proposed system is invest...

The Density Theorem for Gabor Frames is one of the fundamental results of time-frequency analysis. This expository survey attempts to reconstruct the long and very involved history of this theorem and to present its context and evolution, from the onedimensional rectangular lattice setting, to arbitrary lattices in higher dimensions, to irregular Gabor frames, and most recently beyond the setti...

the construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. we apply this system as basis functions to solve the fractional differential and integro-differential equations. biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. some test pr...

A general class of (multiple) hypergeometric type integrals associated with the Jacobi theta functions is defined. These integrals are related to theta hypergeometric series via the residue calculus. In the one variable case, theta function extensions of the Meijer function are obtained. A number of multiple generalizations of the elliptic beta integral associated with the root systems An and C...

The field of implicit complexity has recently produced several bounded-complexity programming languages. This kind of language allows to implement exactly the functions belonging to a certain complexity class. We here present a realizability semantics for a higher-order functional language based on a fragment of linear logic called LAL which characterizes the complexity class PTIME. This langua...

A restarted nonsymmetric Lanczos algorithm is given for computing eigenvalus and both right and left eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Restarting also makes it possible to deal with roundoff error in new ways. We give a scheme for avoiding near-breakdown and discuss maintaining biorthogonality. A system of linear equations can be solved s...

We construct operationally-based realizability relations between phrases in a language with both universal and existential types and programs for a variant SECD machine. The relations, defined using parametricity, biorthogonality and step-indexing, give extensional and compositional specifications of when low-level code and values realize typed source-level terms. We prove full functional corre...

Wavelet analysis has become a developing branch of mathematics for over twenty years. In this paper, the notion of orthogonal nonseparable bivariate wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is proposed by virtue of analogy method and iteration method. Their biorthogonality traits are researched by using time-frequency analysis approach and variable sepa...

We define a general class of (multiple) integrals of hypergeometric type associated with the Jacobi theta functions. These integrals are related to theta hypergeometric series through the residue calculus. In the one variable case, we get theta function extensions of the Meijer function. A number of multiple generalizations of the elliptic beta integral [S2] associated with the root systems An ...