Numerische Mathematik, ISSN 0029-599X, 06/2017, Volume 136, Issue 2, pp. 411 - 438

Journal Article

Geometric and Functional Analysis, ISSN 1016-443X, 8/2013, Volume 23, Issue 4, pp. 1262 - 1277

Journal Article

Acta Mathematica Sinica, English Series, ISSN 1439-8516, 6/2019, Volume 35, Issue 6, pp. 721 - 727

Let Λ ⊂ ℝn be a uniformly discrete set and let C Λ be the vector space consisting of all mean periodic functions whose spectrum is simple and contained in Λ....

trigonometric sums | 42A32 | 42B10 | Mathematics, general | Mean periodic functions | Mathematics | almost periodic functions | MATHEMATICS | MATHEMATICS, APPLIED | Periodic functions

trigonometric sums | 42A32 | 42B10 | Mathematics, general | Mean periodic functions | Mathematics | almost periodic functions | MATHEMATICS | MATHEMATICS, APPLIED | Periodic functions

Journal Article

MICHIGAN MATHEMATICAL JOURNAL, ISSN 0026-2285, 2010, Volume 59, Issue 1, pp. 143 - 151

Journal Article

Journal of Interdisciplinary Mathematics, ISSN 0972-0502, 05/2019, Volume 22, Issue 4, pp. 551 - 566

In this paper, X.Z. Krasniqi modified trigonometric since sum is extended from one dimensions to three dimensions and the integrability and L 1 - rough...

1 | triple trigonometric series | integrability | 42A20 | convergence | 42A32 | conjugate Dirichlet kernel | Fejer kernel | 42A16 | L | Triple sequence

1 | triple trigonometric series | integrability | 42A20 | convergence | 42A32 | conjugate Dirichlet kernel | Fejer kernel | 42A16 | L | Triple sequence

Journal Article

Annals of Probability, ISSN 0091-1798, 2016, Volume 44, Issue 1, pp. 684 - 738

We discuss stochastic calculus for large classes of Gaussian processes, based on rough path analysis. Our key condition is a covariance measure structure...

SPDE | Fractional stochastic heat equation | Random Fourier series | Rough paths | Cameron-Martin regularity | Gaussian processes | fractional stochastic heat equation | INTEGRABILITY | SPDES | random Fourier series | STATISTICS & PROBABILITY | DIFFERENTIAL-EQUATIONS DRIVEN | rough paths | Cameron–Martin regularity | 42A32 | 60G17 | 60H15 | 60G15

SPDE | Fractional stochastic heat equation | Random Fourier series | Rough paths | Cameron-Martin regularity | Gaussian processes | fractional stochastic heat equation | INTEGRABILITY | SPDES | random Fourier series | STATISTICS & PROBABILITY | DIFFERENTIAL-EQUATIONS DRIVEN | rough paths | Cameron–Martin regularity | 42A32 | 60G17 | 60H15 | 60G15

Journal Article

Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 18

In this paper we introduce new classes of p-bounded variation sequences and give a sufficient and necessary condition for weighted integrability of...

42A20 | Analysis | 42A32 | Weighted L p $L^{p}$ integrability | Mathematics, general | Mathematics | Applications of Mathematics | 41A50 | 42A16 | Trigonometric series | Sequences of p -bounded variation | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | Sequences of p-bounded variation | Weighted L-p integrability | Coefficient of variation | Sequences

42A20 | Analysis | 42A32 | Weighted L p $L^{p}$ integrability | Mathematics, general | Mathematics | Applications of Mathematics | 41A50 | 42A16 | Trigonometric series | Sequences of p -bounded variation | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | Sequences of p-bounded variation | Weighted L-p integrability | Coefficient of variation | Sequences

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 04/2014, Volume 287, Issue 5-6, pp. 518 - 529

In this article, we establish a norm equivalence satisfied by general monotone sequences. This is then used to show norm equivalences involving such sequences...

norm inequalities | General monotone sequences | trigonometric series | 42A32 | Norm inequalities | Trigonometric series | MATHEMATICS | FOURIER-SERIES

norm inequalities | General monotone sequences | trigonometric series | 42A32 | Norm inequalities | Trigonometric series | MATHEMATICS | FOURIER-SERIES

Journal Article

Analysis Mathematica, ISSN 0133-3852, 6/2018, Volume 44, Issue 2, pp. 163 - 183

We prove that there is a sequence of trigonometric polynomials with positive integer coefficients, which converges to zero almost everywhere. We also prove...

convergence almost everywhere | approximation | 41A46 | Analysis | L p space | 42A32 | trigonometric polynomial with positive integer coefficients | Mathematics | sum of shifts | 42A05 | space | MATHEMATICS | L-p space

convergence almost everywhere | approximation | 41A46 | Analysis | L p space | 42A32 | trigonometric polynomial with positive integer coefficients | Mathematics | sum of shifts | 42A05 | space | MATHEMATICS | L-p space

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 4/2019, Volume 45, Issue 2, pp. 519 - 561

In this paper, a deterministic sparse Fourier transform algorithm is presented which breaks the quadratic-in-sparsity runtime bottleneck for a large class of...

Sparse Fourier transform (SFT) | Visualization | Computational Mathematics and Numerical Analysis | Structured sparsity | 65T50 | 65T40 | Mathematical and Computational Biology | Mathematics | 68W25 | Computational Science and Engineering | Deterministic constructions | 05-04 | 42A15 | 42A10 | 42A32 | Approximation algorithms | Mathematical Modeling and Industrial Mathematics | 42A16 | 94A12 | MATHEMATICS, APPLIED | Fourier transformations | Algorithms | Research | Periodic functions | Mathematical research

Sparse Fourier transform (SFT) | Visualization | Computational Mathematics and Numerical Analysis | Structured sparsity | 65T50 | 65T40 | Mathematical and Computational Biology | Mathematics | 68W25 | Computational Science and Engineering | Deterministic constructions | 05-04 | 42A15 | 42A10 | 42A32 | Approximation algorithms | Mathematical Modeling and Industrial Mathematics | 42A16 | 94A12 | MATHEMATICS, APPLIED | Fourier transformations | Algorithms | Research | Periodic functions | Mathematical research

Journal Article

Journal of Fourier Analysis and Applications, ISSN 1069-5869, 8/2018, Volume 24, Issue 4, pp. 1072 - 1097

In this paper we study trigonometric series with general monotone coefficients, i.e., satisfying $$\begin{aligned} \sum \limits _{k=n}^{2n} |a_k - a_{k+1}| \le...

General and weak monotonicity | Mathematics | Fourier coefficients | Lebesgue and Lorentz type estimates | Abstract Harmonic Analysis | Salem–Hardy type asymptotic results | Mathematical Methods in Physics | Fourier Analysis | Signal,Image and Speech Processing | 42A32 | Approximations and Expansions | 42A16 | Partial Differential Equations | Salem-Hardy type asymptotic results | MATHEMATICS, APPLIED | APPROXIMATION | THEOREMS | TRIGONOMETRIC SERIES

General and weak monotonicity | Mathematics | Fourier coefficients | Lebesgue and Lorentz type estimates | Abstract Harmonic Analysis | Salem–Hardy type asymptotic results | Mathematical Methods in Physics | Fourier Analysis | Signal,Image and Speech Processing | 42A32 | Approximations and Expansions | 42A16 | Partial Differential Equations | Salem-Hardy type asymptotic results | MATHEMATICS, APPLIED | APPROXIMATION | THEOREMS | TRIGONOMETRIC SERIES

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 8/2014, Volume 143, Issue 2, pp. 422 - 438

Let $${\{\lambda_j\}^\infty_{j=0}}$$ { λ j } j = 0 ∞ be a strictly increasing sequence of positive numbers with λ0 = 0 and λ1 = 1. We use orthogonal Dirichlet...

Dirichlet polynomial | 11L03 | 42A32 | orthogonal polynomial | Mathematics, general | zeta function | Mathematics | mean value | 42C05 | POLYNOMIALS | MATHEMATICS

Dirichlet polynomial | 11L03 | 42A32 | orthogonal polynomial | Mathematics, general | zeta function | Mathematics | mean value | 42C05 | POLYNOMIALS | MATHEMATICS

Journal Article

Analysis Mathematica, ISSN 0133-3852, 12/2017, Volume 43, Issue 4, pp. 641 - 655

We obtain a necessary and sufficient condition for the sums f or g of cosine or sine series with general monotone coefficients to belong to the Lorentz space...

primary 42A32 | secondary 42A16 | Analysis | general monotone sequence | Mathematics | Lorentz space | cosine and sine series | MATHEMATICS | INTEGRABILITY | FOURIER-SERIES | TRIGONOMETRIC SERIES

primary 42A32 | secondary 42A16 | Analysis | general monotone sequence | Mathematics | Lorentz space | cosine and sine series | MATHEMATICS | INTEGRABILITY | FOURIER-SERIES | TRIGONOMETRIC SERIES

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 4/2014, Volume 142, Issue 2, pp. 468 - 474

This note presents two versions of an interesting theorem due to Le and Zhou [4], utilizing a new condition of bounded variation type for a trigonometric...

bounded variation | Mathematics, general | Mathematics | monotone sequence | 26A45 | 42A32 | MATHEMATICS | SINE SERIES | COEFFICIENTS | UNIFORM-CONVERGENCE | TRIGONOMETRIC SERIES

bounded variation | Mathematics, general | Mathematics | monotone sequence | 26A45 | 42A32 | MATHEMATICS | SINE SERIES | COEFFICIENTS | UNIFORM-CONVERGENCE | TRIGONOMETRIC SERIES

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 8/2017, Volume 152, Issue 2, pp. 404 - 420

A trigonometric series strongly bounded at two points and with coefficients forming a log-quasidecreasing sequence is necessarily the Fourier series of a...

26A45 | 42A32 | 46A45 | generalized variation | Mathematics, general | Mathematics | trigonometric series | strong convergence | MATHEMATICS | FOURIER-SERIES | BANACH-SPACES | Mathematics - Classical Analysis and ODEs

26A45 | 42A32 | 46A45 | generalized variation | Mathematics, general | Mathematics | trigonometric series | strong convergence | MATHEMATICS | FOURIER-SERIES | BANACH-SPACES | Mathematics - Classical Analysis and ODEs

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 10/2013, Volume 141, Issue 1, pp. 150 - 160

We generalize a theorem of Leindler while the series is under the condition of MVBVS∗, and investigate the relation between the best approximation of functions...

strong mean value bounded variation | best approximation | 42A20 | 42A32 | Mathematics, general | Mathematics | Fourier coefficient | MATHEMATICS | INTEGRABILITY

strong mean value bounded variation | best approximation | 42A20 | 42A32 | Mathematics, general | Mathematics | Fourier coefficient | MATHEMATICS | INTEGRABILITY

Journal Article

17.
Full Text
An application of MVBV condition in real sense for L 1-convergence of trigonometric series

Acta Mathematica Hungarica, ISSN 0236-5294, 12/2014, Volume 144, Issue 2, pp. 416 - 424

We continue to investigate the application of the Mean Value Bounded Variation (MVBV) concept in real sense, and prove the necessary and sufficient condition...

mean value bounded variation | 42A20 | positivity | 42A32 | Mathematics, general | L 1 -convergence | Mathematics | monotonicity | L | convergence | MATHEMATICS | L-1-convergence

mean value bounded variation | 42A20 | positivity | 42A32 | Mathematics, general | L 1 -convergence | Mathematics | monotonicity | L | convergence | MATHEMATICS | L-1-convergence

Journal Article

18.
Full Text
On L 1-convergence of Fourier series of complex valued functions under the GM7 condition

Acta Mathematica Hungarica, ISSN 0236-5294, 10/2011, Volume 133, Issue 1, pp. 92 - 102

Let f∈L 2π be a real-valued even function with its Fourier series $\frac {a_{0}}{2}+\sum\limits_{n=1}^{\infty}{a_{n}}\cos nx$ , and let S n (f,x) be the nth...

Mathematics, general | L 1 -convergence | Mathematics | Fourier series | 42A20 | 42A32

Mathematics, general | L 1 -convergence | Mathematics | Fourier series | 42A20 | 42A32

Journal Article

Positivity, ISSN 1385-1292, 3/2017, Volume 21, Issue 1, pp. 329 - 342

We supply a Fourier characterization for the real, continuous, isotropic and strictly positive definite kernels on a product of circles. In other words, if...

Strictly positive definite | 65T40 | 33C55 | Positive definite | 42A82 | Mathematics | 43A35 | Isotropy | Product of circles | Skolem-Mahler-Lech theorem | Operator Theory | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | 42A32 | 33C50 | Schoenberg’s theorem | Econometrics | 42A16 | 41A05 | 42B05 | MATHEMATICS | Schoenberg's theorem | SPACES | SPHERES | Studies | Harmonic analysis | Mathematics - Classical Analysis and ODEs

Strictly positive definite | 65T40 | 33C55 | Positive definite | 42A82 | Mathematics | 43A35 | Isotropy | Product of circles | Skolem-Mahler-Lech theorem | Operator Theory | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | 42A32 | 33C50 | Schoenberg’s theorem | Econometrics | 42A16 | 41A05 | 42B05 | MATHEMATICS | Schoenberg's theorem | SPACES | SPHERES | Studies | Harmonic analysis | Mathematics - Classical Analysis and ODEs

Journal Article

Analysis Mathematica, ISSN 0133-3852, 12/2016, Volume 42, Issue 4, pp. 371 - 385

Odd, 2π-periodical, continuous functions represented by Fourier series are considered. The question of the convergence in the metric L of trigonometric...

42A24 | interpolation polynomial | 42A15 | Analysis | 42A10 | 42A32 | Mathematics | convergence in the metric L | Fourier series | 42A16 | MATHEMATICS | Functions (mathematics) | Interpolation | Mathematical analysis | Fourier analysis | Polynomials | Continuity (mathematics) | Convergence

42A24 | interpolation polynomial | 42A15 | Analysis | 42A10 | 42A32 | Mathematics | convergence in the metric L | Fourier series | 42A16 | MATHEMATICS | Functions (mathematics) | Interpolation | Mathematical analysis | Fourier analysis | Polynomials | Continuity (mathematics) | Convergence

Journal Article

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