Boas–Kac roots of positive definite functions of several variables
Tóm tắt
Từ khóa
Tài liệu tham khảo
N. N. Andreev, An extremal problem for periodical functions with small support, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1 (1997), 29–32 (in Russian); translation in Moscow Univ. Math. Bull., 52 (1997), 29–32.
V. V. Arestov and E. E. Berdysheva, Turán’s problem for positive definite functions with supports in a hexagon, Trudy Inst. Mat. Mekh., 7 (2001), 21–29 (in Russian); translated in Proc. Steklov Inst. Math., Suppl. 1 (2001), S20–S29.
V. V. Arestov and E. E. Berdysheva, The Turán problem for a class of polytopes, East J. Approx., 8 (2002), 381–388.
E. E. Berdysheva and H. Berens, On a discrete Turán problem for l1 radial functions, in: New Perspectives on Approximation and Sampling Theory–Festschrift in honor of Paul Butzer’s 85th birthday, Ed. by G. Schmeisser and A. Zayed, Applied and Numerical Harmonic Analysis, Birkhauser (2014), pp. 447–468.
R. P. Boas, Jr. and M. Kac, Inequalities for Fourier transforms of positive functions, Duke Math. J., 12 (1945), 189–206.
A. V. Efimov, An analog of Rudin’s theorem for continuous radial positive definite functions of several variables, Trudy Inst. Mat. Mekh. Ural’sk. Otdel. Ross. Akad. Nauk, 18 (2012), 172–179 (in Russian); translated in Proc. Steklov Inst. Math., 284 (2014), Suppl. 1, 79–86.
W. Ehm, T. Gneiting and D. Richards, Convolution roots of radial positive definite functions with compact support, Trans. Amer. Math. Soc., 356 (2004), 4655–4685.
D. V. Gorbachev, Extremum problem for periodic functions supported in a ball, Math. Notes, 69 (2001), 313–319.
V. I. Ivanov, On the Turán and Delsarte problems for periodic positive definite functions, Math. Notes, 80 (2006), 875–880.
G. Pólya and G. Szegő, Problems and Theorems in Analysis, Vol. 2, Springer (Berlin, 1972); Nauka (Moscow, 1978).
M. N. Kolountzakis and Sz. Gy. Révész, Turán’s extremal problem for positive definite functions on groups, J. London Math. Soc., 74 (2006), 475–496.
Sz. Gy. Révész, Turán’s extremal problem on locally compact abelian groups, Anal. Math., 37 (2011), 15–50.
L. I. Ronkin, Introduction to the Theory of Entire Functions of Several Variables, Nauka (Moscow, 1971) (in Russian); translated in Translations of Mathematical Monographs, Vol. 44, Amer. Math. Soc. (Providence, RI, 1974).
L. I. Ronkin, Entire functions, in: Current problems in mathematics. Fundamental directions, Vol. 9, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform. (Moscow, 1986), pp. 5–36.
C. L. Siegel, Über Gitterpunkte in konvexen Körpern und damit zusammenhängendes Extremalproblem, Acta Math., 65 (1935), 307–323.
S. B. Stechkin, A certain extremal problem for trigonometric series with nonnegative coefficients, Acta Math. Acad. Sci. Hungar., 23 (1972), 289–291.
E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press (Princeton, NJ, 1971); Mir (Moscow, 1974).
W. Stoll, Ganze funktionen endlicher ordnung mit gegebenen nullstellenflächen, Math. Z., 57 (1953), 211–237.
A. M. Yaglom, Correlation Theory of Stationary Random Functions with Examples from Meteorology, Gidrometeoizdat (Leningrad, 1981) (in Russian).