Abel Type Theorems for the Wavelet Transform through the Quasiasymptotic Boundedness
نویسندگان
چکیده
We analyze quasiasymptotic boundedness of distributions and their wavelet transforms, in general, as well as for a class of α− exponentially bounded distributions and their wavelet transforms in particular. The main idea of this paper is to use, instead of the quasiasymptotic behaviour, the notion of quasiasymptotic boundedness. In this way we obtain new Abelian type theorems for the wavelet transform of distributions with different growth. AMS Mathematics Subject Classification (2010): 46F12, 42C40
منابع مشابه
QUASIASYMPTOTIC IN D ′ L q(Rn) 1
The multiresolution expansion {Ejf}j∈N, f ∈ D Lq (R), 1 ≤ q ≤ ∞, is defined via a scaling function which order of regularity is equal to the order of f. Abelian and Tauberian type theorems for the quasiasymptotic behavior at infinity of distributions from D Lq (R) related to the quasiasymptotic behavior at infinity of its projections Ejf, j ∈ N, are given. AMS Mathematics Subject Classification...
متن کاملTauberian-type theorems with application to the Stieltjes transformation
The Abelian and Tauberian-type theorems were introduced by Stanković [7] and Pilipović et al. [5]. In the first part of this paper, we give the definition of the quasiasymptotic expansion at 0+ and the quasiasymptotic behaviour of distributions at infinity from S′+ introduced in [1]. In this paper, we give the definition of space L′(r), classical Stieltjes transformation, modified Stieltjes tra...
متن کاملDe-Noising SPECT Images from a Typical Collimator Using Wavelet Transform
Introduction: SPECT is a diagnostic imaging technique the main disadvantage of which is the existence of Poisson noise. So far, different methods have been used by scientists to improve SPECT images. The Wavelet Transform is a new method for de-noising which is widely used for noise reduction and quality enhancement of images. The purpose of this paper is evaluation of noise reduction in SPECT ...
متن کاملDamage Detection in Post-tensioned Slab Using 2D Wavelet Transforms
Earthquake force, loading more than structural capacity, cracking, material fatigue and the other unpredicted events were undeniable in the structure life cycle in order that environmental conditions of the structure would be changed and treats health. Damage of structures such as crack, corrosion of the post tension cables from inappropriate grouting of the post tension structures and etc. can...
متن کاملThe Effect of Rainfall Parameters on Runoff Using Wavelet Coherence Measure
In this research wavelet coherence measure is implemented for evaluating the relations and effect of rainfall parameters over many years on runoff fluctuations that is for testing proposed linkages between two time series. In this way, monthly Hydro climatological as 3 rainfall stations, one runoff in the outlet of Ardabil plain were used. The results illustrate that 8-12 and 8-16 month modes o...
متن کامل