Displaying similar documents to “The Affine Frame in p -adic Analysis”

Weyl-Heisenberg frame in p -adic analysis

Minggen Cui, Xueqin Lv (2005)

Annales mathématiques Blaise Pascal

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In this paper, we establish an one-to-one mapping between complex-valued functions defined on R + ∪ { 0 } and complex-valued functions defined on p -adic number field Q p , and introduce the definition and method of Weyl-Heisenberg frame on hormonic analysis to p -adic anylysis.

Wavelets with composite dilations.

Guo, Kanghui, Labate, Demetrio, Lim, Wang-Q, Weiss, Guido, Wilson, Edward (2004)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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On the relationship between quasi-affine systems and the à trous algorithm.

Brody Dylan Johnson (2002)

Collectanea Mathematica

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We seek to demonstrate a connection between refinable quasi-affine systems and the discrete wavelet transform known as the à trous algorithm. We begin with an introduction of the bracket product, which is the major tool in our analysis. Using multiresolution operators, we then proceed to reinvestigate the equivalence of the duality of refinable affine frames and their quasi-affine counterparts associated with a fairly general class of scaling functions that includes the class of compactly...

Bounds on the radius of the p-adic Mandelbrot set

Jacqueline Anderson (2013)

Acta Arithmetica

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Let f ( z ) = z d + a d - 1 z d - 1 + . . . + a 1 z ∈ ℂ p [ z ] be a degree d polynomial. We say f is post-critically bounded, or PCB, if all of its critical points have bounded orbit under iteration of f. It is known that if p ≥ d and f is PCB, then all critical points of f have p-adic absolute value less than or equal to 1. We give a similar result for 1/2d ≤ p < d. We also explore a one-parameter family of cubic polynomials over ℚ₂ to illustrate that the p-adic Mandelbrot set can be quite complicated when p < d, in contrast with the...

Affine frames, GMRA's, and the canonical dual

Marcin Bownik, Eric Weber (2003)

Studia Mathematica

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We show that if the canonical dual of an affine frame has the affine structure, with the same number of generators, then the core subspace V₀ is shift invariant. We demonstrate, however, that the converse is not true. We apply our results in the setting of oversampling affine frames, as well as in computing the period of a Riesz wavelet, answering in the affirmative a conjecture of Daubechies and Han. Additionally, we completely characterize when the canonical dual of a quasi-affine...

On (C,1) summability for Vilenkin-like systems

G. Gát (2001)

Studia Mathematica

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We give a common generalization of the Walsh system, Vilenkin system, the character system of the group of 2-adic (m-adic) integers, the product system of normalized coordinate functions for continuous irreducible unitary representations of the coordinate groups of noncommutative Vilenkin groups, the UDMD product systems (defined by F. Schipp) and some other systems. We prove that for integrable functions σₙf → f (n → ∞) a.e., where σₙf is the nth (C,1) mean of f. (For the character...

On the heights of totally p -adic numbers

Paul Fili (2014)

Journal de Théorie des Nombres de Bordeaux

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Bombieri and Zannier established lower and upper bounds for the limit infimum of the Weil height in fields of totally p -adic numbers and generalizations thereof. In this paper, we use potential theoretic techniques to generalize the upper bounds from their paper and, under the assumption of integrality, to improve slightly upon their bounds.

Heights and totally p-adic numbers

Lukas Pottmeyer (2015)

Acta Arithmetica

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We study the behavior of canonical height functions h ̂ f , associated to rational maps f, on totally p-adic fields. In particular, we prove that there is a gap between zero and the next smallest value of h ̂ f on the maximal totally p-adic field if the map f has at least one periodic point not contained in this field. As an application we prove that there is no infinite subset X in the compositum of all number fields of degree at most d such that f(X) = X for some non-linear polynomial f. This...

Unconditional biorthogonal wavelet bases in L p ( ℝ d )

Waldemar Pompe (2002)

Colloquium Mathematicae

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We prove that a biorthogonal wavelet basis yields an unconditional basis in all spaces L p ( ℝ d ) with 1 < p < ∞, provided the biorthogonal wavelet set functions satisfy weak decay conditions. The biorthogonal wavelet set is associated with an arbitrary dilation matrix in any dimension.