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Avoiding look-ahead in the Lanczos method and Padé approximation

E. Ayachour (1999)

Applicationes Mathematicae

In the non-normal case, it is possible to use various look-ahead strategies for computing the elements of a family of regular orthogonal polynomials. These strategies consist in jumping over non-existing and singular orthogonal polynomials by solving triangular linear systems. We show how to avoid them by using a new method called ALA (Avoiding Look-Ahead), for which we give three principal implementations. The application of ALA to Padé approximation, extrapolation methods and Lanczos method for...

Banach algebras of pseudodifferential operators and their almost diagonalization

Karlheinz Gröchenig, Ziemowit Rzeszotnik (2008)

Annales de l’institut Fourier

We define new symbol classes for pseudodifferential operators and investigate their pseudodifferential calculus. The symbol classes are parametrized by commutative convolution algebras. To every solid convolution algebra 𝒜 over a lattice Λ we associate a symbol class M ∞ , 𝒜 . Then every operator with a symbol in M ∞ , 𝒜 is almost diagonal with respect to special wave packets (coherent states or Gabor frames), and the rate of almost diagonalization is described precisely by the underlying convolution algebra...

Bases d'ondelettes sur les courbes corde-arc, noyau de Cauchy et spaces de Hardy associés.

Pascal Auscher, Philippe Tchamitchian (1989)

Revista Matemática Iberoamericana

Se construyen dos bases incondicionales de L2(R) adaptadas al estudio de la integral de Cauchy sobre una curva cuerda-arco, y se extiende la construcción a L2(Rd). Esto permite obtener una prueba simple del "Teorema T(b)" de G. David, J.L. Journé u S. Semmes. Se define un espacio de Hardy ponderado Hb1(Rd) caracterizado por las bases anteriores. Finalmente se aplican estos métodos al estudio del potencial de doble capa sobre una superficie lipschitziana.

Biorthogonal wavelets, MRA's and shift-invariant spaces

Marcin Bownik, Gustavo Garrigós (2004)

Studia Mathematica

We give a characterization of biorthogonal wavelets arising from MRA's of multiplicity D entirely in terms of the dimension function. This improves the previous characterization in [8] removing an unnecessary angle condition. Besides we characterize Riesz wavelets arising from MRA's, and present new proofs based on shift-invariant space theory, generalizing the 1-dimensional results appearing in [17].

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