The discrete wavelet transform (DWT) is extended to functions on the discrete circle to create a fast and complete discrete periodic wavelet transform (DPWT) for bounded periodic sequences. This extension also solves the problem of non-invertibility that arises in the application of the DWT to finite-dimensional sequences and provides the proper theoretical setting for previous incomplete solut...

Adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals. It permits efficient compression of a variety of signals such as sound and images. The predefined libraries of modulated waveforms include orthogonal wavelet-packets, and localized trigonometric functions, have reasonably well controlled time-freque...

Abstract In this paper we disprove part of a conjecture Lieb and Thirring concerning the best constant in their eponymous inequality. We prove that Lieb–Thirring when eigenvalues Schrödinger operator $$-\Delta +V(x)$$ - ? + V ( x</mml:...

We consider orthonormal expansions where the basis functions are governed by some free parameters. If the basis functions adhere to a certain differential or difference equation, then an expression can be given for a specific enforced convergence rate criterion as well as an upper bound for the quadratic truncation error. This expression is a function of the free parameters and some simple sign...

Paley and Wiener have formulated a criterion for a set of functions {gn} to be "near" a given orthonormal set {/w}. The interest of this criterion is that it guarantees the set {gn} to have expansion properties similar to an orthonormal set. In particular, they show that the set \gn) approximately satisfies Parseval's formula. In the first part of this paper we show that, conversely, if a set {...

A linear operator on a Hilbert space may be approximated with nite matrices by choosing an orthonormal basis of the Hilbert space. For an operator that is not compact such approximations cannot converge in the norm topology on the space of operators. Multiplication operators on spaces of L2 functions are never compact; for them we consider how well the eigenvalues of the matrices approximate th...

The spectral representation for stochastic integration operators with respect to the Wiener process is proposed in form of a composition characteristics used mathematical description control systems. This can be defined relative various orthonormal bases. For given deterministic square-integrable kernels, characteristic operator determined as an infinite random matrix. main applications such su...

We study bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. analyse relations between the matrix coefficients of three term for orthonormal as well structure satisfied by these semiclassical polynomials, also a differential-difference equation is deduced. The extension Painlevé to case and two dimensional version Langmuir lattice are obtained.

Abstract. The evaluation of matrix functions of the form f(A)v, where A is a large sparse or structured symmetric matrix, f is a nonlinear function, and v is a vector, is frequently subdivided into two steps: first an orthonormal basis of an extended Krylov subspace of fairly small dimension is determined, and then a projection onto this subspace is evaluated by a method designed for small prob...