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Journal of Approximation Theory, ISSN 0021-9045, 05/2016, Volume 205, pp. 1 - 24
We establish formulas for the b-adic Walsh coefficients of functions in Cα[0,1] for an integer α≥1 and give upper bounds on the Walsh coefficients of these... 
Walsh coefficient | Walsh series | Sobolev space | Smooth function | MATHEMATICS | ORDER | DISCREPANCY BOUNDS | DIGITAL SEQUENCES | F-2 | RULES | Mathematics - Numerical Analysis
Journal Article
Siberian Mathematical Journal, ISSN 0037-4466, 5/2016, Volume 57, Issue 3, pp. 505 - 512
We prove that, given a sequence {ak}k=1 ∞ with a k ↓ 0 and {ak}k=1 ∞ ∉ l 2, reals 0 < ε < 1 and p ∈ [1, 2], and f ∈ L p(0, 1), we can find f ∈ L p(0, 1) with... 
Mathematics, general | Mathematics | 1) space | Fourier coefficients | L p | Walsh system | SYSTEM | MATHEMATICS | SERIES | CONVERGENCE | L-p(0,1) space | NONLINEAR APPROXIMATION
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 12/2009, Volume 80, Issue 3, pp. 430 - 453
We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further,... 
smooth function | wavelet | Walsh coefficient | Walsh series | sobolev space | MATHEMATICS | INTEGRATION | SPACES | RULES
Journal Article
Journal of Contemporary Mathematical Analysis, ISSN 1068-3623, 1/2016, Volume 51, Issue 1, pp. 21 - 33
The paper proves that for any ε > 0 there exists ameasurable set E ⊂ [0, 1] with measure |E| > 1 − ε such that for each f ∈ L1[0, 1] there is a function... 
Mathematics, general | Mathematics | Fourier coefficients | Walsh system | convergence in L 1 -norm | convergence in L | norm | MATHEMATICS | convergence in L-1-norm | Fourier analysis | Research | Mathematical research | Walsh functions
Journal Article
Discrete Mathematics and Applications, ISSN 0924-9265, 10/2016, Volume 26, Issue 5, pp. 259 - 272
We obtain achievable lower and upper bounds for the sums of modules of Walsh coefficients of Boolean functions of nvariables. An average value of such sums in... 
Boolean functions | filtering generators | Walsh coefficients
Journal Article
Designs, Codes and Cryptography, ISSN 0925-1022, 11/2014, Volume 73, Issue 2, pp. 299 - 318
Journal Article
Numerische Mathematik, ISSN 0029-599X, 10/2011, Volume 119, Issue 2, pp. 271 - 297
Journal Article
Hiroshima Mathematical Journal, ISSN 0018-2079, 07/2017, Volume 47, Issue 2, pp. 155 - 179
In this paper we give a new Koksma-Hlawka type inequality for QuasiMonte Carlo (QMC) integration. QMC integration of a function f :[0; 1)(s) -> R by a finite... 
Koksma-Hlaka inequality | Walsh coefficients | Quasi-Monte Carlo integration | SMOOTH FUNCTIONS | SPACES | ALGORITHMS | POINT SETS | MATHEMATICS | ORDER | POLYNOMIAL LATTICE RULES | CONSTRUCTION | ERROR | EFFICIENT
Journal Article
Sbornik Mathematics, ISSN 1064-5616, 2012, Volume 203, Issue 9, pp. 1295 - 1309
The paper is concerned with the behaviour of the coefficients of multiple Walsh-Paley series that are cube convergent to a finite sum. It is shown that even an... 
Cube convergence | Multiple Walsh-Paley series | Cantor-Lebesgue theorem | MATHEMATICS | multiple Walsh-Paley series | cube convergence | TRIGONOMETRIC SERIES | UNIQUENESS
Journal Article
Applicable Algebra in Engineering, Communication and Computing, ISSN 0938-1279, 12/2011, Volume 22, Issue 5, pp. 359 - 366
Journal Article
Journal of Mathematical Sciences (Japan), ISSN 1340-5705, 2016, Volume 23, Issue 4, pp. 727 - 740
Journal Article
Sbornik Mathematics, ISSN 1064-5616, 2012, Volume 203, Issue 3, pp. 351 - 379
This work continues the author's investigations of the convergence of greedy algorithms from the standpoint of classical results on correction of functions. In... 
Greedy algorithm | Correction of functions | Fourier coefficients | Nonlinear approximation | MATHEMATICS | WALSH SYSTEM | RESPECT | nonlinear approximation | SERIES | correction of functions | CONVERGENCE | greedy algorithm | L-P
Journal Article
Symmetry, ISSN 2073-8994, 12/2019, Volume 12, Issue 1, p. 52
Proof of ownership on multimedia data exposes users to significant threats due to a myriad of transmission channel attacks over distributed computing... 
fast walsh–hadamard transform | coefficient ordering | gaussian mapping | singular value decomposition | key mapping
Journal Article
Journal of Computer and System Sciences, ISSN 0022-0000, 2011, Volume 77, Issue 6, pp. 1039 - 1053
A k-bounded pseudo-Boolean function is a real-valued function on { 0 , 1 } n that can be expressed as a sum of functions depending on at most k input bits. The... 
Pseudo-Boolean function | Walsh analysis | Graph finding | Fourier coefficients | Learning polynomials | Linkage discovery | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COMPUTER SCIENCE, THEORY & METHODS | EFFICIENT | DNF | Algorithms | Queries | Equivalence | Upper bounds | Mathematical analysis | Images | Fourier analysis | Mathematical models
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 10/2012, Volume 82, Issue 10, pp. 1815 - 1822
This work is concerned with robust estimation in a semiparametric varying-coefficient partially linear model when the underlying error distribution deviates... 
Walsh-average | Robust nonparametric regression | Semiparametric composite quantile estimator | Asymptotic efficiency | Local linear regression | PARTIALLY LINEAR-MODELS | STATISTICS & PROBABILITY | SELECTION | EFFICIENT
Journal Article
Russian Mathematics, ISSN 1066-369X, 8/2013, Volume 57, Issue 8, pp. 10 - 19
We consider Fourier coefficients for functions of bounded variation with respect to general orthonormal systems (GONS). We show that in general case the... 
Walsh system | trigonometric system | Mathematics, general | Mathematics | Haar system | Fourier series | Fourier coefficients
Journal Article
Proceedings of SPIE - The International Society for Optical Engineering, ISSN 0277-786X, 2015, Volume 9255
Conference Proceeding
Cryptography and Communications, ISSN 1936-2447, 12/2014, Volume 6, Issue 4, pp. 335 - 358
Journal Article
Journal of the Korean Statistical Society, ISSN 1226-3192, 03/2015, Volume 44, Issue 1, pp. 95 - 110
A shrinkage-type variable selection procedure for varying coefficient models is routinely established in the least-squares (LS) framework. Although the LS... 
Walsh-average | Oracle property | Asymptotic relative efficiency | Varying coefficient model | Variable selection | Robust BIC-type criterion | STATISTICS & PROBABILITY | LONGITUDINAL DATA | COMPOSITE QUANTILE REGRESSION | ORACLE PROPERTIES | SHRINKAGE | LASSO | EFFICIENT | Research | Variables (Mathematics) | Mathematical research | Least squares
Journal Article
Journal of Nonparametric Statistics, ISSN 1048-5252, 01/2014, Volume 26, Issue 1, pp. 187 - 206
Journal Article
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