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It has been proved recently that the two-direction refinement equation of the form $f (x) = \sum_{n \in} c_{n, 1} f (k x - n) + \sum_{n \in ℤ} c_{n, - 1} f (- k x - n)$ 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 $f (x) = \sum_{n \in ℤ} c ₙ f (k x - n)$ , which has been used in many areas of mathematics with important applications. The following continuous extension of the classical refinement equation $f (x) = \int_{ℝ} c (y) f (k x - y) d y$ has also various interesting applications....

Reflections on Value Regions, Limit Regions and Truncation Errors for Continued Fractions.

Egil Rye, Haakon Waadeland (1985)

Numerische Mathematik

Regions of Convergence for Hypergeometric Series in Three Variables.

Per W. Karlsson (1974)

Mathematica Scandinavica

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 $x_{j k} : (j, k) \in ℕ ²$ 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 $x_{j k} : k \in ℕ$ is statistically convergent to some $ξ_{j} \in ℂ$ for each fixed j ∈ ℕ ∖ ₁, (iii) the single sequence $x_{j k} : j \in ℕ$ is statistically convergent to some $η_{k} \in ℂ$ for...

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Rad prevrátených hodnôt všetkých prvočísel a niektoré výsledky o konvergencii čiastočných radov harmonického radu

Radon Measures on ß N Associated with Simple Riesz-Means.

Ramanujan's evaluations of Rogers-Ramanujan type continued fractions at primitive roots of unity

Ramanujan's harmonic number expansion into negative powers of a triangular number.

Randomly Weighted Series of Contractions in Hilbert Spaces.

Rate of convergence of summation-integral type operators with derivatives of bounded variation.

Rate preservation of double sequences under $l$ - $l$ type transformation.

Ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces

Rational sequences converging to $π$ .

Recent Results in the Theory of Matrix Transformations in Sequence Spaces

Recherches sur les fractions continues

Recherches sur les fractions continues [ suite et fin ]

Refinement type equations: sources and results

Reflections on Value Regions, Limit Regions and Truncation Errors for Continued Fractions.

Regions of Convergence for Hypergeometric Series in Three Variables.

Regular statistical convergence of double sequences

Regularity of “F” method of summability of sequences.

Relations between sequences and selection properties.

Remark on a formula of P.H. Jackson

Remark on a theorem of K. M. Slipenčuk in the theory of summability of series

Currently displaying 1 – 20 of 35