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Refinement type equations: sources and results

Rafał Kapica, Janusz Morawiec (2013)

Banach Center Publications

It has been proved recently that the two-direction refinement equation of the form f ( x ) = n c n , 1 f ( k x - n ) + n c n , - 1 f ( - k x - n ) can be used in wavelet theory for constructing two-direction wavelets, biorthogonal wavelets, wavelet packages, wavelet frames and others. The two-direction refinement equation generalizes the classical refinement equation f ( x ) = n c f ( k x - n ) , which has been used in many areas of mathematics with important applications. The following continuous extension of the classical refinement equation f ( x ) = c ( y ) f ( k x - y ) d y has also various interesting applications....

Regular statistical convergence of double sequences

Ferenc Móricz (2005)

Colloquium Mathematicae

The concepts of statistical convergence of single and double sequences of complex numbers were introduced in [1] and [7], respectively. In this paper, we introduce the concept indicated in the title. A double sequence x j k : ( j , k ) ² is said to be regularly statistically convergent if (i) the double sequence x j k is statistically convergent to some ξ ∈ ℂ, (ii) the single sequence x j k : k is statistically convergent to some ξ j for each fixed j ∈ ℕ ∖ ₁, (iii) the single sequence x j k : j is statistically convergent to some η k for...

Currently displaying 361 – 380 of 574