On Fourier Series in Several Variables

The aim of the tutorial is to help students to master the basic concepts and methods of the study of calculus. In volume 2 we study analytic geometry in space; differential calculus of functions of several variables; local, conditional, global extrema of functions of several variables; multiple, curvilinear and surface integrals; elements of field theory; numerical, power series, Taylor series and Maclaurin, and Fourier series; applications to the analysis and solution of applied problems. Great attention is paid to comparison of these methods, the proper choice of study design tasks, analyze complex situations that arise in the study of these branches of mathematical analysis. For self-training and quality control knowledge given test questions. For teachers, students and postgraduate students studying mathematical analysis.

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Continuity in $ \Lambda$-variation of functions of several variables and convergence of multiple Fourier series

Sbornik Mathematics ◽

10.1070/sm2002v193n12abeh000697 ◽

2002 ◽

Vol 193 (12) ◽

pp. 1731-1748 ◽

Cited By ~ 4

Author(s):

A N Bakhvalov

Keyword(s):

Fourier Series ◽

Multiple Fourier Series ◽

Several Variables

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Conjugate Fourier Series and Integrals of Several Variables in the L-1 Sense

Proceedings of the Second ISAAC Congress - International Society for Analysis, Applications and Computation ◽

10.1007/978-1-4613-0269-8_5 ◽

2000 ◽

pp. 31-39

Author(s):

Zhong Kai Li

Keyword(s):

Fourier Series ◽

Conjugate Fourier Series ◽

Several Variables

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On pointwise convergence of Fourier series of radial functions in several variables

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-99-04886-8 ◽

1999 ◽

Vol 127 (10) ◽

pp. 2987-2994 ◽

Cited By ~ 3

Author(s):

Shigehiko Kuratsubo

Keyword(s):

Fourier Series ◽

Pointwise Convergence ◽

Radial Functions ◽

Several Variables

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Some properties of an odd-dimensional space

Georgian Mathematical Journal ◽

10.1515/gmj-2019-2067 ◽

2020 ◽

Vol 27 (2) ◽

pp. 321-330

Author(s):

Vakhtang Tsagareishvili

Keyword(s):

Fourier Series ◽

Absolute Convergence ◽

Dimensional Space ◽

Multiple Fourier Series ◽

Partial Derivatives ◽

Several Variables ◽

The Absolute ◽

Series Of Functions ◽

Russian Math

AbstractIn this paper, we investigate the absolute convergence of Fourier series of functions in several variables for an odd-dimensional space when these functions have continuous partial derivatives. It should be noted that similar properties for an even-dimensional space were given in [L. D. Gogoladze and V. S. Tsagareishvili, On absolute convergence of multiple Fourier series (in Russian), Izv. Vyssh. Uchebn. Zaved. Mat. 2015, 9, 12–21; translation in Russian Math. (Iz. VUZ) 59 (2015), no. 9, 9–17]. The obtained results are the best possible in a certain sense.

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