Georgian Mathematical Journal, ISSN 1072-947X, 09/2018, Volume 25, Issue 3, pp. 481 - 491

In this paper, we obtain sufficiency conditions for generalized β-absolute convergence ( ) of single and multiple Fourier series of functions of the class and...

42B99 | 26A16 | 26B30 | Absolute convergence | 42A20

42B99 | 26A16 | 26B30 | Absolute convergence | 42A20

Journal Article

STUDIA MATHEMATICA, ISSN 0039-3223, 2019, Volume 247, Issue 3, pp. 273 - 283

We consider the space A(T-d) of absolutely convergent Fourier series on the torus T-d. The norm on A(T-d) is naturally defined by parallel to f parallel to(A)...

MATHEMATICS | superposition operators | absolutely convergent Fourier series | Beurling-Helson theorem | Mathematics - Classical Analysis and ODEs

MATHEMATICS | superposition operators | absolutely convergent Fourier series | Beurling-Helson theorem | Mathematics - Classical Analysis and ODEs

Journal Article

Georgian Mathematical Journal, ISSN 1072-947X, 03/2019, Volume 26, Issue 1, pp. 117 - 124

In the present paper the sufficient conditions are obtained for the generalized -absolute convergence ( ) of the single Fourier trigonometric series in terms...

26A16 | Absolute convergence | modulus of variation of function | 42A20 | MATHEMATICS | modulus of delta-variation

26A16 | Absolute convergence | modulus of variation of function | 42A20 | MATHEMATICS | modulus of delta-variation

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 12/2018, Volume 156, Issue 2, pp. 361 - 374

We obtain a sufficient condition for the weighted β-absolute convergence of the multiple Fourier series $$\sum_{k_{1} \in\mathbb{Z}} \cdots \sum_{k_{N}...

42B99 | 26B30 | 42A20 | Mathematics, general | Mathematics | multiple Fourier series | 42A16 | absolute convergence | functions of generalized bounded variation

42B99 | 26B30 | 42A20 | Mathematics, general | Mathematics | multiple Fourier series | 42A16 | absolute convergence | functions of generalized bounded variation

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 2/2018, Volume 154, Issue 1, pp. 199 - 214

The assertion that the Salem test [5] for the uniform convergence of a trigonometric Fourier series is improvable, is proved. In particular, an example of a...

42A20 | uniform convergence | Salem test | Mathematics, general | Mathematics | trigonometric Fourier series | 42B05 | MATHEMATICS | CONVERGENCE | Resveratrol

42A20 | uniform convergence | Salem test | Mathematics, general | Mathematics | trigonometric Fourier series | 42B05 | MATHEMATICS | CONVERGENCE | Resveratrol

Journal Article

Journal of Mathematical Sciences, ISSN 1072-3374, 9/2019, Volume 241, Issue 3, pp. 354 - 363

The Lebesgue constant corresponding to the classical Fourier operator is approximated by a family of logarithmic functions depending on two parameters. We find...

Lebesgue constant | asymptotic formula | 42A20 | partial sum | estimate | Mathematics, general | extremal problem | Mathematics | 57Q55 | Fourier operator | Fourier series | norm

Lebesgue constant | asymptotic formula | 42A20 | partial sum | estimate | Mathematics, general | extremal problem | Mathematics | 57Q55 | Fourier operator | Fourier series | norm

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 04/2019, Volume 30, Issue 4, pp. 334 - 346

Let be the orthonormal polynomials with respect to the Sobolev-type inner product where . We obtain necessary and sufficient conditions for the uniform...

Jacobi polynomials | Primary: 42A20 | Sobolev polynomials | partial sum operator | Sobolev-type inner product | Secondary: 33C47 | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | NORM | Fourier series | Sobolev space | Polynomials

Jacobi polynomials | Primary: 42A20 | Sobolev polynomials | partial sum operator | Sobolev-type inner product | Secondary: 33C47 | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | NORM | Fourier series | Sobolev space | Polynomials

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

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

Journal of Fourier Analysis and Applications, ISSN 1069-5869, 12/2018, Volume 24, Issue 6, pp. 1539 - 1553

The paper introduces a variable exponent space X which has in common with $$L^{\infty }([0,1])$$ L ∞ ( [ 0 , 1 ] ) the property that the space C([0, 1]) of...

Hardy–Littlewood maximal function | Mathematics | Abstract Harmonic Analysis | Mathematical Methods in Physics | Fourier Analysis | Signal,Image and Speech Processing | 42A20 | Banach function space | 46E30 | Approximations and Expansions | a.e. divergent Fourier series | Partial Differential Equations | Variable Lebesgue spaces

Hardy–Littlewood maximal function | Mathematics | Abstract Harmonic Analysis | Mathematical Methods in Physics | Fourier Analysis | Signal,Image and Speech Processing | 42A20 | Banach function space | 46E30 | Approximations and Expansions | a.e. divergent Fourier series | Partial Differential Equations | Variable Lebesgue spaces

Journal Article

Mathematische Annalen, ISSN 0025-5831, 12/2013, Volume 357, Issue 4, pp. 1329 - 1361

We prove a vector-valued version of Carleson’s theorem: let $$Y=[X,H]_\theta $$ be a complex interpolation space between an unconditionality of martingale...

Mathematics, general | Mathematics | 42A50 | 42A20 | MATHEMATICS

Mathematics, general | Mathematics | 42A50 | 42A20 | MATHEMATICS

Journal Article

Numerical Algorithms, ISSN 1017-1398, 1/2018, Volume 77, Issue 1, pp. 111 - 150

This paper presents a new approach to improve the order of approximation of the Bernstein operators. Three new operators of the Bernstein-type with the degree...

Bernstein Theorem | Numeric Computing | Korovkin Theorem | Theory of Computation | Linear positive operator | Voronovkaja Theorem | The Bernstein operators | 65D30 | Algorithms | Algebra | 42A20 | Numerical Analysis | Computer Science | 41A10 | Degree of convergence | Rate of convergence | MATHEMATICS, APPLIED | ASYMPTOTIC-EXPANSION

Bernstein Theorem | Numeric Computing | Korovkin Theorem | Theory of Computation | Linear positive operator | Voronovkaja Theorem | The Bernstein operators | 65D30 | Algorithms | Algebra | 42A20 | Numerical Analysis | Computer Science | 41A10 | Degree of convergence | Rate of convergence | MATHEMATICS, APPLIED | ASYMPTOTIC-EXPANSION

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 10/2013, Volume 141, Issue 1, pp. 113 - 126

We introduce the Λ2-strong convergence of numerical sequences and with it we generalize the concept of Λ-strong convergence of the results published by...

Mathematics, general | Mathematics | Λ-strong convergence | Fourier series | 42A20 | numerical sequence

Mathematics, general | Mathematics | Λ-strong convergence | Fourier series | 42A20 | numerical sequence

Journal Article

14.
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 | convergence | MATHEMATICS | L-1-convergence

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

Journal Article

Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, 12/2019, Volume 10, Issue 4, pp. 837 - 854

Let $$\mathcal {L}=-\Delta + \mu $$ L = - Δ + μ be the generalized Schrödinger operator on $$\mathbb {R}^d$$ R d , $$d\ge 3 $$ d ≥ 3 , where $$\Delta $$ Δ is...

35J10 | Bilinear operators | Riesz transform | Mathematics | Operator Theory | Algebra | Functional Analysis | 42A30 | 42A20 | Analysis | Applications of Mathematics | Schrödinger operators | Partial Differential Equations | Hardy space | MATHEMATICS | Schrodinger operators | MATHEMATICS, APPLIED | Schrodinger equation | Research | Mathematical research | Operator theory

35J10 | Bilinear operators | Riesz transform | Mathematics | Operator Theory | Algebra | Functional Analysis | 42A30 | 42A20 | Analysis | Applications of Mathematics | Schrödinger operators | Partial Differential Equations | Hardy space | MATHEMATICS | Schrodinger operators | MATHEMATICS, APPLIED | Schrodinger equation | Research | Mathematical research | Operator theory

Journal Article

Computational Methods and Function Theory, ISSN 1617-9447, 6/2019, Volume 19, Issue 2, pp. 227 - 236

A simple and direct proof is given of a generalization of a classical result on the convergence of $$\sum _{k=0}^\infty a_k \text{ e }^{i k x}$$ ∑ k = 0 ∞ a k...

Primary 30B10 | Computational Mathematics and Numerical Analysis | Functions of a Complex Variable | Mathematics | 30H25 | Trigonometric series | Convergence of Taylor series | Exceptional sets | Dirichlet-type spaces | Analytic Besov spaces | Capacity | 42A20 | Analysis | MATHEMATICS | MATHEMATICS, APPLIED

Primary 30B10 | Computational Mathematics and Numerical Analysis | Functions of a Complex Variable | Mathematics | 30H25 | Trigonometric series | Convergence of Taylor series | Exceptional sets | Dirichlet-type spaces | Analytic Besov spaces | Capacity | 42A20 | Analysis | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Inverse Problems in Science and Engineering, ISSN 1741-5977, 04/2019, Volume 27, Issue 4, pp. 460 - 483

The main goal of this paper is applying the cut-off projection for solving one-dimensional backward heat conduction problem in a two-slab system with a perfect...

cut-off projection | 42A20 | regularized solution | ill-posedness | 35K05 | Two-slab system | 65J20 | backward heat conduction problem | error estimates | 47A52 | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | TIME | PARABOLIC EQUATIONS BACKWARD | FUNDAMENTAL-SOLUTIONS | Conductive heat transfer | Cut-off | Conduction heating | Projection | Qualitative analysis | Fourier series | Frequency stability

cut-off projection | 42A20 | regularized solution | ill-posedness | 35K05 | Two-slab system | 65J20 | backward heat conduction problem | error estimates | 47A52 | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | TIME | PARABOLIC EQUATIONS BACKWARD | FUNDAMENTAL-SOLUTIONS | Conductive heat transfer | Cut-off | Conduction heating | Projection | Qualitative analysis | Fourier series | Frequency stability

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2018, Volume 14

We study the partial sum operator for a Sobolev-type inner product related to the classical Gegenbauer polynomials. A complete characterization of the partial...

Sobolev polynomials | Gegenbauer polynomials | Partial sum operator | Sobolev-type inner product | EXPANSIONS | MEAN CONVERGENCE | GENERALIZED JACOBI SERIES | PHYSICS, MATHEMATICAL | partial sum operator | INTERPOLATING POLYNOMIALS | Mathematics - Functional Analysis

Sobolev polynomials | Gegenbauer polynomials | Partial sum operator | Sobolev-type inner product | EXPANSIONS | MEAN CONVERGENCE | GENERALIZED JACOBI SERIES | PHYSICS, MATHEMATICAL | partial sum operator | INTERPOLATING POLYNOMIALS | Mathematics - Functional Analysis

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

Publicacions Matematiques, ISSN 0214-1493, 2019, Volume 63, Issue 1, pp. 155 - 182

We extend Rubio de Francia's extrapolation theorem for functions valued in UMD Banach function spaces, leading to short proofs of some new and known results....

Hardy-Littlewood maximal function | P-convexity | Extrapolation | Fourier multipliers | Littlewood-Paley-Rubio de Francia inequalities | Banach function spaces | Variational Carleson operator | Muckenhoupt weights | UMD | FACTORIZATION | PROPERTY | BANACH-LATTICES | p-convexity | L-P | variational Carleson operator | CALDERON | MATHEMATICS | LITTLEWOOD-PALEY-RUBIO | SEMIGROUPS | REGULARITY | FOURIER MULTIPLIER THEOREMS | OPERATORS

Hardy-Littlewood maximal function | P-convexity | Extrapolation | Fourier multipliers | Littlewood-Paley-Rubio de Francia inequalities | Banach function spaces | Variational Carleson operator | Muckenhoupt weights | UMD | FACTORIZATION | PROPERTY | BANACH-LATTICES | p-convexity | L-P | variational Carleson operator | CALDERON | MATHEMATICS | LITTLEWOOD-PALEY-RUBIO | SEMIGROUPS | REGULARITY | FOURIER MULTIPLIER THEOREMS | OPERATORS

Journal Article

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