Multiple Fourier series and integrals (Q788231)

scientific article; zbMATH DE number 3842454

Language	Label	Description	Also known as
English	Multiple Fourier series and integrals	scientific article; zbMATH DE number 3842454

Statements

instance of

scholarly article

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title

Multiple Fourier series and integrals (English)

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published in

Journal of Soviet Mathematics

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publication date

1984

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review text

Translation from Itogi Nauki Tekh., Ser. Mat. Anal. 19, 3-54 (Russian) (1982; Zbl 0511.42021).

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zbMATH Keywords

survey, multiple Fourier series and integral

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511.42021

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Subsequences of the partial sums of a trigonometric series which are everywhere convergent to zero

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The convergence of the double Fourier series of continuous functions

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Q4065969

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Q3207530

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Lectures on Fourier Integrals. (AM-42)

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Q5559407

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Q5644521

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The question of $A^*$-summability of double trigonometric Fourier series

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Q5683202

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ON THE CONVERGENCE OF RIESZ SPHERICAL MEANS OF MULTIPLE FOURIER SERIES AND INTEGRALS OF FUNCTIONS OF BOUNDED GENERALIZED VARIATION

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Convergence of double Fourier series for functions of bounded generalized variation. I

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On the Gibbs phenomenon for Riesz spherical means of multiple Fourier series and Fourier integrals

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ON CONVERGENCE OF RIESZ SPHERICAL MEANS OF MULTIPLE FOURIER SERIES

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ON THE SUMMABILITY OF FOURIER INTEGRALS BY RIESZ SPHERICAL MEANS

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The Abel-Poisson summation method for multiple Fourier series

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Conjugate functions of several variables in the class Lip alpha

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On multipliers of Fourier integrals in the spaces $L_{p,\theta}$

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The approximation in the $L_p$ metric of differentiable functions of several variables by Fourier sums

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Cantor-Lebesgue theorem for double trigonometric series

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Discrete imbedding theorems and Lebesgue constants

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The approximation of functions of many variables by their Fejer sums

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The multidimensional Jackson theorem

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A lower bound for Lebesgue constants

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On an embedding theorem and uniform convergence of multiple Fourier series

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A divergent multiple Fourier series of power series type

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Convergence and Divergence of Series Conjugate to a Convergent Multiple Fourier Series

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Convergence, summability, and uniqueness of multiple trigonometric series

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Convergence, Uniqueness, and Summability of Multiple Trigonometric Series

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Cesaro Summability of the Conjugate Series and the Double Hilbert Transform

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Q5566665

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Q5574789

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Restricted summation and localization of double trigonometric series

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Contributions to Fourier Analysis. (AM-25)

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Q3229718

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Q5566663

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Q5568697

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On Fourier-Stieltjes Transforms

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On the existence of certain singular integrals

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On Singular Integrals

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On convergence and growth of partial sums of Fourier series

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Oscillatory integrals and multiplier problem for the disc

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Some results on double Fourier series

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Q4102271

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Measurable Functions and Spherical Summability of Multiple Fourier Series

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A Cantor-Lebesgue Theorem in Two Dimensions

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The Cantor-Lebesgue Theorem

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Spherical Convergence and Certain Singular Integrals

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On spherical summation of the Fourier transform of a distribution whose partial derivatives are representable by integration

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On the convergence of multiple Fourier series

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The multiplier problem for the ball

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On the divergence of multiple Fourier series

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A note on spherical summation multipliers

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Convergence on almost every line for functions with gradient in $L^p(R^n)$

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Inequalities for strongly singular convolution operators

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Double Fourier series with coefficients $0(nm)^{-1}$

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Convergence Criteria for Double Fourier Series

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An example of Torrigiani related to multiple Fourier series

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On the localization property of square partial sums for multiple Fourier series

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Some Aspects of Fourier Series

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On localization for double Fourier series

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On Gibbs' phenomenon for Riesz spherical means of multiple Fourier integrals and Fourier series

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A Convergence Theorem for Double L 2 Fourier Series

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Q5571776

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On fourier transforms of radial functions

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On summabilities of double Fourier series

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On the uniqueness of summable trigonometric series and integrals

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Norms of powers of absolutely convergent Fourier series in several variables

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On a multiplier transform

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Prediction theory and Fourier series in several variables

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ON THE MEAN INVERSION OF FOURIER AND HANKEL TRANSFORMS

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Fourier transforms related to convex sets

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On multiplier transformations

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Multiplier transformations. II

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Fourier integral operators. I

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Oscillatory integrals and multipliers on FL$^p$

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On the localization property of multiple Fourier series

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Q4059368

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Functions of L$^p$-multipliers. II

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On Bochner's theorem on the critical index for multiple Fourier series

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On the summation of multiple Fourier series

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Q5683206

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Spherical convergence and integrability of multiple trigonometric series on hypersurfaces

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Generalized Laplacians and Multiple Trigonometric Series

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On Lebesgue Summability for Double Series

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Lebesgue Summability of Double Trigonometric Series

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Summability $R_r$ for double series

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Q4087714

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On formal integration of double trigonometric series

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Q3855654

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Q4153153

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Q3872950

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Spherical Means of Conjugate Fourier Integrals in $E_2 $ at the Critical Index

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Spherical Summability of Conjugate Multiple Fourier Series and Integrals at the Critical Index

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Capacity and absolute Abel summability of multiple Fourier series

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On the Localization of Rectangular Partial Sums for Multiple Fourier Series

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Q4092395

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Q3847544

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Q3847545

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Abel summability of the double series successively derived from the double Fourier series

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Q3280246

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On absolute convergence of double Fourier series with gaps

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On convergence of double Fourier series with gaps of functions of bounded Rth variation

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Notes on Fourier Expansions (II)

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Correction to the Paper "On the Spherical Convergence of Multiple Fourier Series"

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The Fréchet Variation and the Convergence of Multiple Fourier Series

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Q3241339

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On absolute convergence of multiple Fourier series

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L 2 Asymptotes for Fourier Transforms of Surface-Carried Measures

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Q5566664

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A multiplier criterion in Euclidean n-space with applications to Bernstein inequalities

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One point regularity properties of multiple Fourier series with gaps

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Order Summability of Multiple Fourier Series

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Plessner's theorem for Riesz conjugates

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The Abel summability of conjugate multiple Fourier-Stieltjes integrals

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A Tauberian theorem for multiple Fourier series

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Some remarks an interpolation of operators and Fourier coefficients

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A Note on the Uniqueness of Double Trigonometric Series

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An extension of results in the uniqueness theory of double trigonometric series

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Square Summation and Localization of Double Trigonometric Series

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Logarithmic Capacity of Sets and Double Trigonometric Series

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Generalized Laplacians of the second kind and double trigonometric series

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Circular Summability C of Double Trigonometric Series

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Summability and Uniqueness of Double Trigonometric Integrals

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Cantor-type uniqueness of multiple trigonometric integrals

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The Laplacian of Fourier transforms

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Localization of conjugate multiple trigonometric series

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THE UNIQUENESS OF DOUBLE TRIGONOMETRIC SERIES UNDER CIRCULAR CONVERGENCE

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Uniqueness of multiple trigonometric series

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The conjugate Fourier-Stieltjes integral in the plane

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Fourier series in several variables

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Spherical convergence, bounded variation, and singular integrals on the N-torus

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On the harmonic summability of double Fourier series

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On the strong summability of double Fourier series

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Q3289157

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Q3843759

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Q5518572

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The $(L)$ summability of double Fourier series

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Convergence almost everywhere of certain singular integrals and multiple Fourier series

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On the convergence almost everywhere of double Fourier series

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On limits of sequences of operators

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A maximal function with applications to Fourier series

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Localization and summability of multiple Fourier series

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On certain exponential sums arising in multiple Fourier series

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On Absolute Convergence of Multiple Fourier Series

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On double integrals and Fourier series

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Q5581836

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On the Abel summability of multiple Fourier series by spherical means

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Q5641587

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A restriction theorem for the Fourier transform

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Q4093902

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Q4130495

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Some Necessary Conditions for Radial Fourier Multipliers

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Über absolute Summierbarkeit von $n$-dimensionalen Fourierreihen und Fourierintegralen

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Q4080131

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Gibbs Phenomenon for Functions of Two Variables

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Convergence of the Hausdorff Means of Double Fourier Series<sup>*</sup>

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Gibbs phenomenon for the Hausdorff means of double sequences

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Convergence of double Fourier series

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The Hausdorff means of double-Fourier series and the principle of localization

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Special trigonometric series in 𝑘-dimensions

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On the summation of conjugate Fourier integrals of functions of several variables

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On summability methods for conjugate Fourier-Stieltjes integrals in several variables and generalizations

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Summability of double Fourier series

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Riesz-Bochner summability of Fourier integrals and Fourier series

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Norm Convergence of Riesz-Bochner Means For Radial Functions

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Absolute Abel Summability and Capacity

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On the Summability, by Spherical Riesz means, of Multiple Fourier Series

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On the Summability, by Spherical Riesz Means, of Derived Multiple Fourier Series

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A Cantor-Lebesgue theorem for double trigonometric series

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On Fourier coefficients and transforms of functions of two variables

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On the Summability of Multiple Fourier Series

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On the boundary values of functions of several complex variables, I

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full work available at URL

https://doi.org/10.1007/bf01305756

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Identifiers

zbMATH Open document ID

0531.42003

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DOI

10.1007/BF01305756

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:788231