Literature cited
V. A. Il'in, “Localization and convergence problems for Fourier series with respect to a fundamental system of functions of the Laplace operator,” Usp. Mat. Nauk,23, No. 2, 61–120 (1968).
V. A. Il'in, “Conditions for the convergence of spectral expansions that correspond to self-adjoint extensions of elliptic operators. IV. Theorems of negative type for an arbitrary extension of a general second order self-adjoint elliptic operator,” Differents. Uravn.,9, No. 1, 49–73 (1973).
Sh. A. Alimov, V. A. Il'in, and E. M. Nikishin, “Convergence problems of multiple trigonometric series and spectral expansions. I; II,” Usp. Mat. Nauk,31, No. 6 (192), 28–83 (1976);32, No. 1 (193), 107–130 (1977).
V. A. Il'in, “Necessary and sufficient conditions for the basis property and the equiconvergence with a trigonometric series of spectral expansions. I; II,” Differents. Uravn.,16, No. 5, 771–794; No. 6, 980–1009 (1980).
V. A. Il'in, “On the summability of Fourier series of eigenfunctions by Riesz, Cesaro, and Poisson-Abel means,” Differents. Uravn.,2, No. 6, 816–827 (1966).
V. A. Il'in, “Necessary and sufficient conditions for the basis property and the equiconvergence with a trigonometric series of spectral expansions in systems of exponentials,” Dokl. Akad. Nauk SSSR,273, No. 4, 789–793 (1983).
R. E. A. C. Paley and N. Wiener, Fourier Transforms in the Complex Domain, Am. Math. Soc., New York (1934).
N. Levinson, Gap and Density Theorems, Am. Math. Soc., New York (1940).
R. J. Duffin and A. C. Schaeffer, “A class of nonharmonic Fourier series,” Trans. Am. Math. Soc.,72, No. 2, 341–366 (1952).
S. Verblunsky, “On an expansion in exponential series,” Quart. J. Math. Oxford (2),7, 231–240 (1956).
S. Verblunsky, “On a class of integral functions,” Quart. J. Math. Oxford (2),8, 312–320 (1957).
V. A. Molodenkov, “Equisummability in the sense of M. Riesz of expansions in certain systems of exponential functions,” Mat. Zametki,15, No. 3, 381–386 (1974).
N. K. Nikol'skii, B. S. Pavlov, and S. V. Khrushchev, Unconditional bases of exponential and reproducing kernels. I. Preprint LOMI R-8-80, Leningrad (1980).
A. M. Sedletskii, “Expansions in exponential functions,” Sib. Mat. Zh.,16, No. 4, 820–829 (1975).
A. M. Sedletskii, “Biorthogonal expansions of functions in exponential series on intervals of the real axis,” Usp. Mat. Nauk,37, No. 5 (227), 51–95 (1982).
T. A. Samarskaya, “On the uniform equiconvergence of expansions with respect to a system of exponential functions and in trigonometric Fourier series,” Mat. Zametki,37, No. 4, 532–544 (1985).
Ya. Sh. Salimov, “The analogue of the multidimensional discontinuous Dirichlet factor for Riesz means in the complex domain,” Mat. Zametki,40, No. 4, 492–510 (1986).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 41, No. 1, pp. 57–70, January, 1987.
The author is grateful to V. A. Il'in and E. I. Moiseev for the detailed discussion of the results of this paper.
Rights and permissions
About this article
Cite this article
Salimov, Y.S. Equiconvergence of the Riesz means of expansions, corresponding to an N-fold system of exponents and to the N-fold fourier integral. Mathematical Notes of the Academy of Sciences of the USSR 41, 35–44 (1987). https://doi.org/10.1007/BF01159527
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01159527