Analytic Fourier Transforms and Exponential Approximations.~I

A. M. Sedletskii

Contemporary Mathematics. Fundamental Directions, Analytic Fourier transforms and exponential approximations. I, Tome 5 (2003), pp. 3-152.

Bibliographie

[1] Akhiezer N. I., Lektsii po teorii approksimatsii, Nauka, M., 1965 | MR

[2] Berg I., Lëfstrëm I., Interpolyatsionnye prostranstva. Vvedenie, Mir, M., 1980 | MR

[3] Garnett Dzh., Ogranichennye analiticheskie funktsii, Mir, M., 1984 | MR | Zbl

[4] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR

[5] Goldberg A. A., Ostrovskii I. V., Raspredelenie znachenii meromorfnykh funktsii, Nauka, M., 1970 | MR

[6] Zigmund A., Trigonometricheskie ryady, t. 1, Mir, M., 1965 | MR

[7] Zigmund A., Trigonometricheskie ryady, t. 2, Mir, M., 1965 | MR

[8] Ilin V. A., “Neobkhodimye i dostatochnye usloviya bazisnosti v $L_p$ i ravnoskhodimosti s trigonometricheskim ryadom spektralnykh razlozhenii po sisteme eksponent”, Dokl. AN SSSR, 273:4 (1983), 789–793 | MR | Zbl

[9] Katsnelson V. E., “O raspolozhenii v kompleksnoi ploskosti nulei preobrazovaniya Fure”, Dokl. AN SSSR, 171:2 (1966), 272–274 | MR | Zbl

[10] Krein S. G. (red.), Funktsionalnyi analiz, Nauka, M., 1972 | MR | Zbl

[11] Kusis P., Vvedenie v teoriyu prostranstv $H^p$, Mir, M., 1984 | MR

[12] Levin B. Ya., Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956

[13] Levin B. Ya., “O bazisakh pokazatelnykh funktsii v $L^2$”, Zap. matem. otd. fiz.-mat. fak-ta KhGU i KhMO, Ser. 4, 27 (1961), 39–48

[14] Levin B. Ya., “Interpolyatsiya tselymi funktsiyami eksponentsialnogo tipa”, Matem. fizika i funkts. anal., vyp. 1, FTINT AN USSR, 1969, 136–146 | MR

[15] Leontev A. F., “O svoistvakh posledovatelnostei polinomov Dirikhle, skhodyaschikhsya na intervale mnimoi osi”, Izv. AN SSSR, ser. matem., 29:2 (1965), 269–328 | MR | Zbl

[16] Leontev A. F., Ryady eksponent, Nauka, M., 1976 | MR

[17] Leontev A. F., Posledovatelnost polinomov iz eksponent, Nauka, M., 1980 | MR

[18] Milman V. D., “Geometricheskaya teoriya prostranstv Banakha”, Uspekhi matem. nauk, 25:3 (1970), 113–174 | MR | Zbl

[19] Molodenkov V. A., “O razlozheniyakh po sobstvennym funktsiyam odnoi kraevoi zadachi”, Diff. uravn. i vychisl. matem., vyp. 2, SGU, 1975, 56–65 | MR

[20] Molodenkov V. A., “Ravnosummiruemost po M. Rissu razlozhenii po nekotorym sistemam pokazatelnykh funktsii”, Matem. zametki, 15:3 (1974), 381–386 | MR | Zbl

[21] Natanson I. P., Konstruktivnaya teoriya funktsii, Gostekhizdat, M., 1949

[22] Sedletskii A. M., “O funktsiyakh, periodicheskikh v srednem”, Izv. AN SSSR, ser. matem., 34:6 (1970), 1391–1415

[23] Sedletskii A. M., “Negarmonicheskie ryady Fure”, Sib. matem. zhurn., 12:5 (1971), 1100–1114 | MR | Zbl

[24] Sedletskii A. M., “O biortogonalnykh razlozheniyakh po pokazatelnym funktsiyam”, Izv. AN SSSR, ser. matem., 36:3 (1972), 583–590 | MR | Zbl

[25] Sedletskii A. M., “Polnye i ravnomerno minimalnye sistemy pokazatelnykh funktsii v $L^p(-\pi,\pi)$”, Trudy MEI, 1972, no. 146, 167–174

[26] Sedletskii A. M., “Polnye i minimalnye sistemy eksponent v prostranstvakh $L^p(-\pi,\pi)$, $1\le p\le 2$”, Trudy MEI, 1976, no. 290, 63–69 | MR

[27] Sedletskii A. M., “Izbytki sistem pokazatelnykh funktsii”, Matem. zametki, 22:6 (1977), 803–814 | Zbl

[28] Sedletskii A. M., “Ob odnom klasse biortogonalnykh razlozhenii po pokazatelnym funktsiyam”, Izv. AN SSSR, ser. matem., 41:2 (1977), 393–415 | MR | Zbl

[29] Sedletskii A. M., “O polnote sistem eksponent v prostranstvakh differentsiruemykh funktsii”, Trudy MEI, 1977, no. 334, 98–103

[30] Sedletskii A. M., “O raznosti izbytkov dvukh sistem pokazatelnykh funktsii”, Trudy MEI, 1978, no. 357, 98–102 | MR

[31] Sedletskii A. M., “Izbytki sistem eksponentsialnykh funktsii”, Izv. AN SSSR, ser. matem., 44:1 (1980), 203–218 | MR | Zbl

[32] Sedletskii A. M., “Biortogonalnye razlozheniya v ryady eksponent na intervalakh veschestvennoi osi”, Uspekhi matem. nauk, 37:5 (1982), 51–95 | MR

[33] Sedletskii A. M., “Izbytki blizkikh sistem eksponent v $L^p$”, Sib. matem. zhurn., 24:4 (1983), 164–175 | MR | Zbl

[34] Sedletskii A. M., “O chisto mnimykh vozmuscheniyakh pokazatelei $\lambda_n$ v sisteme $\{\exp(i\lambda_n t)\}$”, Sib. matem. zhurn., 26:4 (1985), 151–158 | MR | Zbl

[35] Sedletskii A. M., “O polnote i neminimalnosti sistem eksponent v $L^p(-\pi,\pi)$”, Sib. matem. zhurn., 29:1 (1988), 159–170 | MR

[36] Sedletskii A. M., “O ravnomernoi skhodimosti negarmonicheskikh ryadov Fure”, Tr. MIAN, 200, 1991, 299–309 | MR | Zbl

[37] Sedletskii A. M., “O nulyakh preobrazovaniya Fure finitnoi mery”, Matem. zametki, 53:1 (1993), 111–120 | MR

[38] Sedletskii A. M., “Negarmonicheskie ryady Fure bez svoistva Rimana–Lebega”, Izv. RAN, ser. matem., 58:6 (1994), 123–136 | MR | Zbl

[39] Sedletskii A. M., “Razlozheniya po sobstvennym funktsiyam operatora differentsirovaniya s razmazannym kraevym usloviem”, Diff. uravn., 30:1 (1994), 70–76 | MR

[40] Sedletskii A. M., “O chisle nulei tseloi funktsii, chasto vstrechayuscheisya v negarmonicheskom analize”, Vestnik MEI, 1994, no. 4, 85–88 | MR

[41] Sedletskii A. M., “Approksimativnye svoistva sistem eksponent v $L^p(a,b)$”, Diff. uravn., 31:10 (1995), 1639–1645 | MR | Zbl

[42] Sedletskii A. M., “Kogda vse nuli tseloi funktsii eksponentsialnogo tipa lezhat v krivolineinoi poluploskosti (neobkhodimoe uslovie)”, Matem. sb., 186:9 (1995), 125–134 | MR | Zbl

[43] Sedletskii A. M., “Postroenie polnykh minimalnykh, no ne ravnomerno minimalnykh v $L^p$ i $C$ sistem eksponent s otdelimym veschestvennym spektrom”, Matem. zametki, 58:4 (1995), 582–595 | MR | Zbl

[44] Sedletskii A. M., “O tselykh funktsiyakh klassa S. N. Bernshteina, ne yavlyayuschikhsya preobrazovaniyami Fure–Stiltesa”, Matem. zametki, 61:3 (1997), 367–380 | MR | Zbl

[45] Sedletskii A. M., “O prinadlezhnosti vsekh nulei finitnogo preobrazovaniya Fure krivolineinoi poluploskosti”, Trudy 2-go Mezhdunar. seminara «Diff. uravn. i ikh pril.» (Samara, 1998), 152–158 | Zbl

[46] Sedletskii A. M., “Ob ustoichivosti ravnomernoi minimalnosti sistemy eksponent”, Metrich. teor. funktsii i smezhn. vopr. analiza, AFTs, M., 1999, 221–237 | MR

[47] Sedletskii A. M., “Bazisy, vstrechayuschiesya pri reshenii uravnenii smeshannogo tipa”, Diff. uravn., 35:4 (1999), 507–515 | MR

[48] Seneta E., Pravilno menyayuschiesya funktsii, Nauka, M., 1985 | MR | Zbl

[49] Skokov A. V., “O biortogonalnykh razlozheniyakh integriruemykh funktsii v ryady eksponent”, Vestnik MEI, 1994, no. 4, 89–94 | MR

[50] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR

[51] Titchmarsh E. K., Vvedenie v teoriyu integralov Fure, Gostekhizdat, M., 1948

[52] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, t. 2, Mir, M., 1984

[53] Khardi G. Kh., Rogozinskii V. V., Ryady Fure, Fizmatgiz, M., 1959

[54] Kheifits A. I., “Kharakteristika nulei nekotorykh spetsialnykh klassov tselykh funktsii konechnoi stepeni”, Teor. funktsii, funkts. anal. i ikh pril., Kharkov, 9 (1968), 3–13

[55] Edvards R., Ryady Fure v sovremennom izlozhenii, t. 2, Mir, M., 1985

[56] Alexander W. O., Redheffer R., “The exess of sets of complex exponentials”, Duke Math. J., 34 (1967), 59–72 | DOI | MR | Zbl

[57] Beurling A., Malliavin P., “On Fourier transforms of measures with compact support”, Acta Math., 107 (1962), 291–309 | DOI | MR | Zbl

[58] Beurling A., Malliavin P., “On the closure of characters and the zeros of entire functions”, Acta Math., 118 (1967), 79–93 | DOI | MR | Zbl

[59] Boas R. P., Entire functions, Academic Press, New York, 1954 | MR | Zbl

[60] Bloom S., “Hardy integral estimates for the Laplace transforms”, Proc. Amer. Math. Soc., 116 (1992), 417–426 | DOI | MR | Zbl

[61] Cartwright M., “The zeros of certain integral functions”, Quart. J. Math., 1 (1930), 38–59 | DOI | Zbl

[62] Doetsch G., Handbuch der Laplace-Transformation, B. 1, Basel, 1950

[63] Duren P. L., Theory of $H^p$ spaces, Academic Press, New York, 1970 | MR

[64] Elsner J., “Zulässige Abänderungen von Exponential-systemen in $L^p(-A,A)$”, Math. Z., 120 (1971), 211–220 | DOI | MR | Zbl

[65] Hardy G. H., Littlewood J. E., “Elementary theorems concerning power series with positive coefficients and moment constants of positive functions”, J. Reine Angew. Math., 157 (1927), 141–158 | Zbl

[66] Ingham A. E., “A note on Fourier transforms”, J. London Math. Soc., 9 (1934), 29–32 | DOI | Zbl

[67] Levinson N., Gap and density theorems, Publ. Amer. Math. Soc., New York, 1940 | MR | Zbl

[68] Luxemburg W. A. J., Korevaar J., “Entire functions and Müntz–Szász type approximation”, Trans. Amer. Math. Soc., 157 (1971), 23–37 | DOI | MR | Zbl

[69] Minkin A. M., “Equiconvergence theorems for differential operators”, J. Math. Sciences, 96:6 (1999), 3631–3715 | DOI | MR | Zbl

[70] Ostrovskii I. V., Peresyolkova I. N., “Nonasymptotic results on distribution of zeros of the function $E_\rho(z;\mu)$”, Anal. Math., 23 (1997), 283–296 | DOI | MR | Zbl

[71] Paley R., Wiener N., Fourier transforms in the complex domain, Publ. Amer. Math. Soc., New York, 1934 | MR | Zbl

[72] Pitt H. R., “Theorems on Fourier series and power series”, Duke Math. J., 3 (1937), 747–755 | DOI | MR | Zbl

[73] Polya G., “Über die Nullstellen gewisser ganzer Funktionen”, Math. Z., 2 (1918), 352–383 | DOI | MR | Zbl

[74] Redheffer R., “Elementary remarks on completeness”, Duke Math. J., 35 (1968), 103–116 | DOI | MR | Zbl

[75] Redheffer R., “Completeness of sets of complex exponentials”, Advanc. Math., 24 (1977), 1–62 | DOI | MR | Zbl

[76] Redheffer R., Young R. M., “Completeness and basis properties of complex exponentials”, Trans. Amer. Math. Soc., 277 (1983), 93–111 | DOI | MR | Zbl

[77] Schwartz L., Étude des sommes d'exponentielles réelles., Hermann, Paris, 1943 | Zbl

[78] Schwartz L., “Théorie génerale des fonctions moyenne-périodiques”, Ann. Math., 48 (1947), 857–918 | DOI | MR

[79] Sedletskii A. M., “On completeness of the systems $\{\exp(ix(n+ih_n))\}$”, Anal. Math. 1978, 4, 125–143 | DOI | MR

[80] Sedletskii A. M., “An analogue of a Hardy–Littlewood theorem for Laplace transform and its applications”, Anal. Math., 11 (1985), 343–354 | DOI | MR

[81] Sedletskii A. M., “On zeros of Laplace transform of finite measure”, Integral Transforms and Special Functions, 1 (1993), 51–59 | DOI | MR

[82] Sedletskii A. M., “Complex variants of Abelian theorem for Laplace transform”, Integral Transforms and Special Functions, 3 (1995), 107–112 | DOI | MR

[83] Sedletskii A. M., “Addition to Polya's theorem on zeros of Fourier sine-transforms”, Integral Transforms and Special Functions, 9 (2000), 65–68 | DOI | MR | Zbl

[84] Sedletskii A. M., Fourier transforms and approximations, Gordon and Breach Science Publishers, Amsterdam, 2000 | MR | Zbl

[85] Stein E., “Interpolation of linear operators”, Trans. Amer. Math. Soc., 83 (1956), 482–492 | DOI | MR | Zbl

[86] Stein E. M., Weiss G., Introduction to Fourier analysis on Euclidean spaces, University Press, Princeton, New York, 1971 | MR

[87] Verblunsky S., “On an expansion on exponential series”, Quart. J. Math., 7:27 (1956), 231–240 | DOI | MR | Zbl

[88] Verblunsky S., “On a class of integral functions”, Quart. J. Math., 8:32 (1957), 312–320 | DOI | MR | Zbl

[89] Young R., “On perturbing bases of complex exponentials in $L^2(-\pi,\pi)$”, Proc. Amer. Math. Soc., 53 (1975), 137–140 | DOI | MR | Zbl

[90] Young R. M., An introduction to nonharmonic Fourier series, Academic Press, New York, 1980 | MR