Literature cited
K. I. Babenko, “On the approximation of a class of periodic functions of several variables by trigonometric polynomials,” Dokl. Akad. Nauk SSSR,132, No. 5, 982–985 (1960).
É. S. Belinskii, “Application of Fourier transform to summability of Fourier series,” Doctoral Dissertation, Physicomathematical Sciences, Donets (1977).
É. S. Belinskii, “On certain properties of hyperbolic partial sums of Fourier series and integrals,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 10, 869–870 (1978).
É. S. Belinskii, “Behavior of the Lebesgue constants of certain methods of summation of multiple Fourier series,” in: Metric Questions of Theory of Functions and Mappings [in Russian], G. D. Suvorov and V. I. Belyi (eds.), Naukova Dumka, Kiev (1977), pp. 19–39.
A. A. Yudin and V. A. Yudin, “Discrete embedding theorems and Lebesgue constants,” Mat. Zametki,22, No. 3, 381–394 (1977).
I. R. Liflyand, The Lebesgue Constants of the Hyperbolic Partial Sums of Multiple Fourier Series [in Russian], Deposited in the All-Union Institute of Scientific and Technical Information at No. 2349-80.
M. V. Fedoryuk, The Saddle-Point Method [in Russian], Nauka, Moscow (1977).
V. A. Il'in, “Problems of localization and convergence for Fourier series of the Laplace operator with respect to the fundamental systems of functions,” Usp. Mat. Nauk,23, No. 2, 61–120 (1968).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 39, No. 5, pp. 674–683, May, 1986.
Rights and permissions
About this article
Cite this article
Liflyand, I.R. Exact order of the lebesgue constants of hyperbolic partial sums of multiple fourier series. Mathematical Notes of the Academy of Sciences of the USSR 39, 369–374 (1986). https://doi.org/10.1007/BF01156675
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01156675