Smooth well-localized Parseval wavelets based on wavelet sets in R

نویسندگان

  • Kathy D. Merrill
  • KATHY D. MERRILL
چکیده

A generalized filter construction is used to build non-MRA Parseval wavelets for dilation by 2 in L2(R2). These examples have the same multiplicity functions as wavelet sets, yet can be made to be Cr with Cr Fourier transform for any fixed positive integer r.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Smooth functions associated with wavelet sets on R, d ≥ 1, and frame bound gaps

The theme is to smooth characteristic functions of Parseval frame wavelet sets by convolution in order to obtain implementable, computationally viable, smooth wavelet frames. We introduce the following: a new method to improve frame bound estimation; a shrinking technique to construct frames; and a nascent theory concerning frame bound gaps. The phenomenon of a frame bound gap occurs when certa...

متن کامل

Orthonormal Dilations of Parseval Wavelets

We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group BS(1, 2) = 〈u, t | utu = t〉. We give a precise description of this representation in some special cases, and show that for wavelet sets, it is related to symbolic dynamics (Theorem 3.14). We show that the structure of the representation depends on the ana...

متن کامل

Minimally Supported Frequency Composite Dilation Parseval Frame Wavelets

Abstract. A composite dilation Parseval frame wavelet is a collection of functions generating a Parseval frame for L2(Rn) under the actions of translations from a full rank lattice and dilations by products of elements of groups A and B. A minimally supported frequency composite dilation Parseval frame wavelet has generating functions whose Fourier transforms are characteristic functions of set...

متن کامل

ar X iv : 0 90 3 . 49 89 v 4 [ m at h . FA ] 1 9 M ay 2 00 9 GABOR FIELDS AND WAVELET SETS FOR THE HEISENBERG GROUP

We study singly-generated wavelet systems on R that are naturally associated with rank-one wavelet systems on the Heisenberg group N . We prove a necessary condition on the generator in order that any such system be a Parseval frame. Given a suitable subset I of the dual of N , we give an explicit construction for Parseval frame wavelets that are associated with I . We say that g ∈ L(I×R) is Ga...

متن کامل

Wavelets with Composite Dilations

A wavelet with composite dilations is a function generating an orthonormal basis or a Parseval frame for L2(Rn) under the action of lattice translations and dilations by products of elements drawn from non-commuting matrix sets A and B. Typically, the members of B are shear matrices (all eigenvalues are one) while the members of A are matrices expanding or contracting on a proper subspace of Rn...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008