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## ‣ Super-wavelets on local fields of positive characteristic

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/11/2015
Português

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The concept of super-wavelet was introduced by Balan, and Han and Larson over
the field of real numbers which has many applications not only in engineering
branches but also in different areas of mathematics. To develop this notion on
local fields having positive characteristic we obtain characterizations of
super-wavelets of finite length as well as Parseval frame multiwavelet sets of
finite order in this setup. Using the group theoretical approach based on coset
representatives, further we establish Shannon type multiwavelet in this
perspective while providing examples of Parseval frame (multi)wavelets and
(Parseval frame) super-wavelets. In addition, we obtain necessary conditions
for decomposable and extendable Parseval frame wavelets associated to Parseval
frame super-wavelets.; Comment: arXiv admin note: text overlap with arXiv:1511.05703

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## ‣ Semi-orthogonal Parseval wavelets associated to GMRAs on local fields of positive characteristics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/11/2015
Português

Relevância na Pesquisa

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In this article we establish theory of semi-orthogonal Parseval wavelets
associated to generalized multiresolution analysis (GMRA) for the local field
of positive characteristics (LFPC). By employing the properties of translation
invariant spaces on the core space of GMRA we obtain a characterization of
semi-orthogonal Parseval wavelets in terms of consistency equation for LFPC. As
a consequence, we obtain a characterization of an orthonormal (multi)wavelet to
be associated with an MRA in terms of multiplicity function as well as
dimension function of a (multi)wavelet. Further, we provide characterizations
of Parseval scaling functions, scaling sets and bandlimited wavelets together
with a Shannon type multiwavelet for LFPC.; Comment: 21 pages

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## ‣ Linear combinations of generators in multiplicatively invariant spaces

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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Multiplicatively invariant (MI) spaces are closed subspaces of
$L^2(\Omega,\mathcal{H})$ that are invariant under multiplications of (some)
functions in $L^{\infty}(\Omega)$. In this paper we work with MI spaces that
are finitely generated. We prove that almost every linear combination of the
generators of a finitely generated MI space produces a new set on generators
for the same space and we give necessary and sufficient conditions on the
linear combinations to preserve frame properties. We then apply what we prove
for MI spaces to system of translates in the context of locally compact abelian
groups and we obtain results that extend those previously proven for systems of
integer translates in $L^2(\mathbb{R}^d)$.; Comment: 13 pages. Minor changes have been made. To appear in Studia
Mathematica

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## ‣ Construction of Biorthogonal Wavelet Packets on Local Fields of Positive Characteristic

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/08/2014
Português

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Orthogonal wavelet packets lack symmetry which is a much desired property in
image and signal processing. The biorthogonal wavelet packets achieve symmetry
where the orthogonality is replaced by the biorthogonality. In the present
paper, we construct biorthogonal wavelet packets on local fields of positive
characteristic and investigate their properties by means of the Fourier
transforms. We also show how to obtain several new Riesz bases of the space
L2(K) by constructing a series of subspaces of these wavelet packets. Finally,
we provide the algorithms for the decomposition and reconstruction using these
biorthogonal wavelet packets.

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## ‣ Characterization of wavelets and MRA wavelets on local fields of positive characteristic

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/12/2013
Português

Relevância na Pesquisa

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We provide a characterization of wavelets on local fields of positive
characteristic based on results on affine and quasi affine frames. This result
generalizes the characterization of wavelets on Euclidean spaces by means of
two basic equations. We also give another characterization of wavelets.
Further, all wavelets which are associated with a multiresolution analysis on a
such a local field are also characterized.; Comment: arXiv admin note: text overlap with arXiv:1103.0090

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