Abel type theorems for the wavelet transform through the quasiasymptotic boundedness

Abstract

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.

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“…The twentieth century is characterized as the century of world population growth and it is considered one of the most significant achievements of civilization, while the twenty-first century is characterized as the century of aging. The global average life expectancy was extended by 5.5 years in the period from 2000 to 2016 (Vukovic, 2021 ), which is the largest increase since the 60s of the twentieth century. According to United Nations projections, the number of people over the age of 60 will more than double by 2050, from the current 840 million to over 2 billion people (Vukovic, 2021 ).…”

“…The global average life expectancy was extended by 5.5 years in the period from 2000 to 2016 (Vukovic, 2021 ), which is the largest increase since the 60s of the twentieth century. According to United Nations projections, the number of people over the age of 60 will more than double by 2050, from the current 840 million to over 2 billion people (Vukovic, 2021 ).…”