Unconditional bases of reproducing kernels in Hilbert spaces of entire functions
Ufa mathematical journal, Tome 5 (2013) no. 3, pp. 67-76 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the existence of unconditional bases of reproducing kernels in a functional Hilbert space of entire functions. It is proved that under certain conditions, unconditional bases of reproducing kernels do not exist. It is shown that in particular spaces some known theorems on the absence of unconditional bases are the consequences of these results.
Keywords: Hilbert spaces, entire functions, reproducing kernels, unconditional bases.
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K. P. Isaev; R. S. Yulmukhametov. Unconditional bases of reproducing kernels in Hilbert spaces of entire functions. Ufa mathematical journal, Tome 5 (2013) no. 3, pp. 67-76. http://geodesic.mathdoc.fr/item/UFA_2013_5_3_a6/

[1] Aronszajn N., “Theory of reproducing kernels”, Transactions of the American Mathematical Society, 68:3 (1950), 337–404 | DOI | MR | Zbl

[2] Nikolskii N. K., Pavlov B. S., Khruschev S. V., Bezuslovnye bazisy iz eksponent i vosproizvodyaschikh yader, I, Preprint, LOMI, 80 pp.

[3] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965, 448 pp. | MR

[4] Nikolskii N. K., Lektsii ob operatore sdviga, Nauka, M., 1980 | MR

[5] Seip K., “Density theorems for sampling and interpolation in the Bargmann–Fock space, I”, Reine Angew. Math., 429 (1992), 91–106 | MR | Zbl

[6] Seip K., Wallsten R., “Density theorems for sampling and interpolation in the Bargmann–Fock space, II”, Reine Angew. Math., 429 (1992), 107–113 | MR | Zbl

[7] Isaev K. P., Yulmukhametov R. S., “Ob otsutstvii bezuslovnykh bazisov iz eksponent v prostranstvakh Bergmana na oblastyakh, ne yavlyayuschikhsya mnogougolnikami”, Izv. RAN. Ser. matem., 71:6 (2007), 69–90 | DOI | MR | Zbl

[8] Borichev A., Dhuez R., Kellay K., “Sampling and interpolation in large Bergman and Fock spaces”, Journal of Functional Analysis, 242:2 (2007), 563–606 | DOI | MR | Zbl

[9] Borichev A., Lyubarskii Yu., “Riesz bases of reproducing kernels in Fock type spaces”, Journal of the Institute of Mathematics of Jussieu, 9 (2010), 449–461 | DOI | MR | Zbl

[10] Yulmukhametov R. S., “Asimptoticheskaya approksimatsiya subgarmonicheskikh funktsii”, Sib. mat. zh., 26:4 (1985), 159–175 | MR | Zbl

[11] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966 | MR | Zbl

[12] Lutsenko V. I., Yulmukhametov R. S., “Obobschenie teoremy Vinera–Peli na funktsionaly v prostranstvakh Smirnova”, Tr. MIAN, 200, 1991, 245–254 | MR | Zbl

[13] Isaev K. P., Yulmukhametov R. S., “Preobrazovaniya Laplasa funktsionalov na prostranstvakh Bergmana”, Izv. RAN. Ser. matem., 68:1 (2004), 5–42 | DOI | MR | Zbl

[14] Lutsenko V. I., Bezuslovnye bazisy iz eksponent v prostranstvakh Smirnova, Dissertatsiya na soiskanie uchenoi stepeni kandidata fiz.-mat. nauk, Institut matematiki s VTs UNTs RAN, 1992

[15] Lutsenko V. I., Yulmukhametov R. S., “Obobschenie teoremy Peli–Vinera na vesovye prostranstva”, Matem. zametki, 48:5 (1990), 80–87 | MR | Zbl

[16] Lutsenko V. I., “Teorema Peli–Vinera na neogranichennom intervale”, Issledovaniya po teorii priblizhenii, Ufa, 1989, 79–85 | MR | Zbl

[17] Napalkov V. V., Bashmakov R. A., Yulmukhametov R. S., “Asimptoticheskoe povedenie integralov Laplasa i geometricheskie kharakteristiki vypuklykh funktsii”, DAN, 413:1 (2007), 20–22 | MR | Zbl

[18] Isaev K. P., Yulmukhametov R. S., “O bezuslovnykh bazisakh iz eksponent v gilbertovykh prostranstvakh”, Ufimskii matematicheskii zhurnal, 3:1 (2011), 3–15 | Zbl