Journal of Statistical Planning and Inference, ISSN 0378-3758, 09/2019

Journal Article

MATHEMATICAL INEQUALITIES & APPLICATIONS, ISSN 1331-4343, 07/2019, Volume 22, Issue 3, pp. 837 - 853

In this article we discuss the behaviour of Theta-means of quadratical partial sums of double Walsh series of a function in L-p(G(2)) (1 <= p <= infinity). In...

Walsh group | approximation | Walsh system | two-dimensional system | MATHEMATICS | weighted mean | quadratical partial sum | Walsh-Fourier series | Theta-mean | Lipschitz function | Norlund mean | modulus of continuity | SUMMABILITY | NORLUND MEANS

Walsh group | approximation | Walsh system | two-dimensional system | MATHEMATICS | weighted mean | quadratical partial sum | Walsh-Fourier series | Theta-mean | Lipschitz function | Norlund mean | modulus of continuity | SUMMABILITY | NORLUND MEANS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 11/2013, Volume 224, pp. 278 - 282

The Hankel matrix has various applications. In this paper we prove that Hankel matrix is strongly regular and apply to obtain the necessary and sufficient...

Hankel matrix | Walsh–Fourier series | Toeplitz matrix | Walsh-Fourier series | MATHEMATICS, APPLIED | APPROXIMATION | Walsh-Fourier

Hankel matrix | Walsh–Fourier series | Toeplitz matrix | Walsh-Fourier series | MATHEMATICS, APPLIED | APPROXIMATION | Walsh-Fourier

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 12/2014, Volume 175, Issue 4, pp. 511 - 518

It is shown that Walsh–Fourier series of $$W$$ W -continuous functions can have maximal sets of limit functions on small subsets of the unit interval.

42C10 | Mathematics, general | Mathematics | Fourier–Walsh series | Walsh–Fourier series | Universality | MATHEMATICS | Fourier-Walsh series | Walsh-Fourier series

42C10 | Mathematics, general | Mathematics | Fourier–Walsh series | Walsh–Fourier series | Universality | MATHEMATICS | Fourier-Walsh series | Walsh-Fourier series

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 03/2016, Volume 144, Issue 3, pp. 1073 - 1085

We consider multipliers for noncommutative Walsh-Fourier series. Let R be the type II1 hyperfinite factor. For x is an element of L-1( R), 0 < alpha < 1, the...

MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | Noncommutative martingales | Walsh-Fourier series | SPACES | multipliers

MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | Noncommutative martingales | Walsh-Fourier series | SPACES | multipliers

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2015, Volume 421, Issue 1, pp. 206 - 214

Almost everywhere strong exponential summability of Fourier series in Walsh and trigonometric systems was established by Rodin in 1990. We prove, that if the...

Walsh series | Strong summability | Everywhere divergent Walsh–Fourier series | Everywhere divergent Walsh-Fourier series

Walsh series | Strong summability | Everywhere divergent Walsh–Fourier series | Everywhere divergent Walsh-Fourier series

Journal Article

Analysis Mathematica, ISSN 0133-3852, 03/2018, Volume 44, Issue 1, pp. 57 - 71

We discuss the behaviour of the Theta-means of Walsh series of a function in L-p (1 <= p <= infinity). We investigate the rate of the approximation by this...

Walsh group | approximation | Walsh system | HARDY-SPACES | MATHEMATICS | weighted mean | Walsh-Fourier series | Theta-mean | COEFFICIENTS | Lipschitz function | Norlund mean | modulus of continuity | SUMMABILITY | NORLUND MEANS

Walsh group | approximation | Walsh system | HARDY-SPACES | MATHEMATICS | weighted mean | Walsh-Fourier series | Theta-mean | COEFFICIENTS | Lipschitz function | Norlund mean | modulus of continuity | SUMMABILITY | NORLUND MEANS

Journal Article

Applied Mathematics and Information Sciences, ISSN 1935-0090, 09/2012, Volume 6, Issue 3, pp. 535 - 538

In this paper we study A-statistical summability of conjugate Fourier series, derived Fourier series and Walsh-Fourier series. At the end of the paper it is...

Fourier series | Walsh-Fourier series | A-statistical convergence | Statistical convergence | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

Fourier series | Walsh-Fourier series | A-statistical convergence | Statistical convergence | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

Journal Article

Analysis Mathematica, ISSN 0133-3852, 03/2018, Volume 44, Issue 1, pp. 73 - 88

For a non-negative integer n let us denote the dyadic variation of a natural number n by V (n) := Sigma(infinity)(j=0)vertical bar n(j)-n(j+1)vertical bar+...

MATHEMATICS | almost everywhere convergence | double Walsh-Fourier series | quadratic partial sum | DIVERGENCE | SQUARE PARTIAL-SUMS

MATHEMATICS | almost everywhere convergence | double Walsh-Fourier series | quadratic partial sum | DIVERGENCE | SQUARE PARTIAL-SUMS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2016, Volume 435, Issue 1, pp. 765 - 782

For functions in Orlicz classes, we consider multiple Walsh–Fourier series for which the rectangular partial sums have indices ( ), where either or components...

Local smoothness condition | Lacunary sequence of rectangular partial sums | Multiple Walsh–Fourier series | Orlicz class | Weak generalized localization almost everywhere | Multiple Walsh-Fourier series | MATHEMATICS | MATHEMATICS, APPLIED | SUBSEQUENCE | SETS | CRITERION | WEAK GENERALIZED LOCALIZATION

Local smoothness condition | Lacunary sequence of rectangular partial sums | Multiple Walsh–Fourier series | Orlicz class | Weak generalized localization almost everywhere | Multiple Walsh-Fourier series | MATHEMATICS | MATHEMATICS, APPLIED | SUBSEQUENCE | SETS | CRITERION | WEAK GENERALIZED LOCALIZATION

Journal Article

Revista Matematica Iberoamericana, ISSN 0213-2230, 2014, Volume 30, Issue 3, pp. 979 - 1014

We prove a variation norm Carleson theorem for Walsh Fourier series of functions with values in certain UMD Banach spaces, sharpening a recent result of...

Walsh-fourier series | Pointwise convergence | Variational norm | P-VARIATION | MARTINGALES | variational norm | SPACES | MODEL | OSCILLATION | MATHEMATICS | WEIGHTED BOUNDS | Walsh-Fourier series | BILINEAR HILBERT TRANSFORM | GROWTH | CONVERGENCE | OPERATORS | Mathematics - Classical Analysis and ODEs

Walsh-fourier series | Pointwise convergence | Variational norm | P-VARIATION | MARTINGALES | variational norm | SPACES | MODEL | OSCILLATION | MATHEMATICS | WEIGHTED BOUNDS | Walsh-Fourier series | BILINEAR HILBERT TRANSFORM | GROWTH | CONVERGENCE | OPERATORS | Mathematics - Classical Analysis and ODEs

Journal Article

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN 0022-247X, 01/2015, Volume 421, Issue 1, pp. 206 - 214

Almost everywhere strong exponential summability of Fourier series in Walsh and trigonometric systems was established by Rodin in 1990. We prove, that if the...

MATHEMATICS | STRONG APPROXIMATION | MATHEMATICS, APPLIED | Walsh series | BMO | Strong summability | Everywhere divergent Walsh-Fourier series

MATHEMATICS | STRONG APPROXIMATION | MATHEMATICS, APPLIED | Walsh series | BMO | Strong summability | Everywhere divergent Walsh-Fourier series

Journal Article

Indian Journal of Mathematics, ISSN 0019-5324, 04/2018, Volume 60, Issue 1, pp. 45 - 63

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 2009, Volume 161, Issue 1, pp. 259 - 279

For any integers necessary and sufficient conditions are given for scaling filters with many terms to generate a -multiresolution analysis in . A method for...

Multifractals | Adapted wavelet analysis | Orthogonal [formula omitted]-wavelets | Lacunary Walsh series | Stability | Walsh–Fourier transform | Orthogonal p-wavelets | Walsh-Fourier transform | MATHEMATICS | CANTOR DYADIC GROUP | ORTHOGONAL WAVELETS

Multifractals | Adapted wavelet analysis | Orthogonal [formula omitted]-wavelets | Lacunary Walsh series | Stability | Walsh–Fourier transform | Orthogonal p-wavelets | Walsh-Fourier transform | MATHEMATICS | CANTOR DYADIC GROUP | ORTHOGONAL WAVELETS

Journal Article

15.
Full Text
Convergence of a Subsequence of Triangular Partial Sums of Double Walsh-Fourier Series

Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), ISSN 1068-3623, 7/2019, Volume 54, Issue 4, pp. 210 - 215

In 1987 Harris proved-among others that for each 1 ≤ p < 2 there exists a two-dimensional function f ∈ L p such that its triangular Walsh-Fourier series does...

42C10 | Mathematics, general | Double Walsh-Fourier series | Mathematics | triangular partial sum | Convergence in measure | MATHEMATICS | DIVERGENCE

42C10 | Mathematics, general | Double Walsh-Fourier series | Mathematics | triangular partial sum | Convergence in measure | MATHEMATICS | DIVERGENCE

Journal Article

Mathematical Notes, ISSN 0001-4346, 1/2013, Volume 93, Issue 1, pp. 332 - 336

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2005, Volume 307, Issue 1, pp. 206 - 218

The boundedness of Marcinkiewicz maximal operator for -dimensional Walsh–Fourier series is studied from the martingale Hardy–Lorentz space into the Lorentz...

Marcinkiewicz–Fejer means | Hardy–Lorentz space | Multiple Walsh–Fourier series | Hardy-Lorentz space | Multiple Walsh-Fourier series | Marcinkiewicz-Fejer means | multiple Walsh-Fourier series | MATHEMATICS | MATHEMATICS, APPLIED | CESARO SUMMABILITY

Marcinkiewicz–Fejer means | Hardy–Lorentz space | Multiple Walsh–Fourier series | Hardy-Lorentz space | Multiple Walsh-Fourier series | Marcinkiewicz-Fejer means | multiple Walsh-Fourier series | MATHEMATICS | MATHEMATICS, APPLIED | CESARO SUMMABILITY

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 2006, Volume 141, Issue 1, pp. 8 - 28

In the paper we prove that the maximal operator of the -means of cubical partial sums of -dimensional Walsh–Fourier series is of weak type (1,1). Moreover, the...

Cesàro means | Almost everywhere convergence | Multiple Walsh–Fourier series | Multiple Walsh-Fourier series | multiple Walsh-Fourier series | MATHEMATICS | almost everywhere convergence | Cesaro means | CESARO SUMMABILITY

Cesàro means | Almost everywhere convergence | Multiple Walsh–Fourier series | Multiple Walsh-Fourier series | multiple Walsh-Fourier series | MATHEMATICS | almost everywhere convergence | Cesaro means | CESARO SUMMABILITY

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 4/2011, Volume 131, Issue 1, pp. 122 - 137

We consider the double Walsh orthonormal system $$\{w_m(x)w_n(y):\, m,n \in \mathbb{N}\}$$ on the unit square $\mathbb{I}^{2}$ , where {w m (x)} is the...

42C10 | dyadic modulus of continuity | dyadic L p -modulus of continuity | double Walsh–Fourier series | 26A16 | Mathematics, general | Mathematics | 26A15 | functions of s -bounded fluctuation | absolute convergence | dyadic Lipschitz classes of functions in two variables | dyadic L | functions of s-bounded fluctuation | double Walsh-Fourier series | modulus of continuity | MATHEMATICS | dyadic L-p-modulus of continuity

42C10 | dyadic modulus of continuity | dyadic L p -modulus of continuity | double Walsh–Fourier series | 26A16 | Mathematics, general | Mathematics | 26A15 | functions of s -bounded fluctuation | absolute convergence | dyadic Lipschitz classes of functions in two variables | dyadic L | functions of s-bounded fluctuation | double Walsh-Fourier series | modulus of continuity | MATHEMATICS | dyadic L-p-modulus of continuity

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 07/2013, Volume 140, Issue 1-2, pp. 162 - 168

The second author recently introduced modified Walsh-Dirichlet kernels which generated filtered Walsh-Fourier series. The purpose of this article is to show...

42C10 | modified Walsh-Dirichlet kernel | 43A75 | Walsh series | filtered Walsh-Fourier series | Walsh function | Rademacher function | MATHEMATICS | Computer science

42C10 | modified Walsh-Dirichlet kernel | 43A75 | Walsh series | filtered Walsh-Fourier series | Walsh function | Rademacher function | MATHEMATICS | Computer science

Journal Article

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