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2. Multidimensional Residues and Applications

Author

Aizenberg, L. A., Tsikh, A. K., Yuzhakov, A. P., Gamkrelidze, R. V., editor, Agrachev, A. A., editor, Gonchar, A. A., editor, Mishchenko, E. F., editor, Ostianu, N. M., editor, Sakharova, V. P., editor, Zhishchenko, A. B., editor, Khenkin, G. M., editor, and Vitushkin, A. G., editor

Published
1994
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3. ℂn

Author

Aizenberg, L. A., Havin, Victor P., editor, and Nikolski, Nikolai K., editor

Published
1994
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8. Encyclopaedia of Mathematics, Supplement III

Author

Abhyankar, S. S., primary, Abramov, V., additional, Adem, A., additional, Aizenberg, L., additional, Albeverio, S., additional, Alías, Luís J., additional, Andréka, H., additional, Apanasov, B. N., additional, Assani, I., additional, Atanassov, K., additional, Axler, S., additional, Bagchi, A., additional, Balachandran, K., additional, Bapat, R. B., additional, Bardos, C., additional, Bartsch, T., additional, Bates, P. W., additional, Belinsky, E. S., additional, Ben-Israel, A., additional, Benguria, R. D., additional, Berg, Ch., additional, Bergelson, V., additional, Beukers, F., additional, Bloch, A., additional, Boley, D. L., additional, de Boor, C., additional, Brasselet, J. -P., additional, Brown, R., additional, Brownawell, W. Dale, additional, Brzezinski, T., additional, Buhmann, M., additional, Bultheel, A., additional, Bump, D., additional, Caenepeel, S., additional, Caflisch, R. E., additional, Calvert, B. D., additional, Carroll, R., additional, Chan, O., additional, Clarke, F., additional, Coelho, Flávio Ulhoa, additional, Collins, D. J., additional, Common, A. K., additional, Coutinho, S. C., additional, Croke, C., additional, Csordas, G., additional, Curto, Raúl E., additional, Dales, H. G., additional, Debnath, L., additional, Deistler, M., additional, Derighetti, A., additional, Deveney, J. K., additional, Dieter, U., additional, Dräxler, P., additional, Drensky, V., additional, Dror, M., additional, Dunkl, C. F., additional, Duval, A., additional, Ehrhardt, T., additional, Eisenberg, B., additional, Elaydi, S., additional, Elizalde, E., additional, Engel, K., additional, Enochs, E., additional, Eytan, M., additional, Fang, Y., additional, Farrell, E. J., additional, López, A. Fernández, additional, Foias, C., additional, Fraenkel, A. S., additional, Fukushima, M., additional, Gannon, T., additional, von zur Gathen, J., additional, Gelbart, S., additional, Gemignani, L., additional, Ghosh, S. K., additional, Glazebrook, J. F., additional, Goerss, P., additional, Goodman, J. E., additional, Gordon, B. Brent, additional, Goto, S., additional, Gottschalk, H., additional, Govaerts, W., additional, Graham, S. W., additional, Grannell, M. J., additional, Griggs, T. S., additional, Grigorchuck, R. I., additional, Grossman, J. W., additional, Gutknecht, M. H., additional, Hahn, U., additional, Harbater, D., additional, Harder, G., additional, Hart, K. P., additional, Haukkanen, P., additional, Heath-Brown, D. R., additional, Helminck, G. F., additional, Hensley, D., additional, Hitchin, N. J., additional, den Hollander, F., additional, Hovenier, J. W., additional, Huang, Y. -Z., additional, Iliev, I. D., additional, Immerman, N., additional, Inuiguchi, M., additional, Isac, G., additional, Ivanov, S. V., additional, Jaco, W., additional, Jacobsen, M., additional, Jarosz, K., additional, Jung, Soon-M., additional, Jungnickel, D., additional, Kamiya, N., additional, Kanamori, A., additional, Kania-Bartoszyńska, J., additional, Kaup, W., additional, Kawamata, Y., additional, Kellay, H., additional, Kenderov, P. S., additional, Kerner, O., additional, Khmaladze, E., additional, Klamka, J., additional, Klin, M., additional, Kłopotek, M. A., additional, Knill, E. H., additional, Knopfmacher, J., additional, Kolountzakis, M. N., additional, Komkov, V., additional, Krzyż, J. G., additional, Kulkarni, S. H., additional, Kung, J. P. S., additional, Kuo, Hui-H., additional, Kuperberg, K. M., additional, Lapidus, M. L., additional, Lazarov, R. D., additional, Lepowsky, J., additional, Li, C. Heng, additional, Liflyand, E. R., additional, Light, W. A., additional, Lukeš, J., additional, Lumiste, Ü., additional, Lychagin, V., additional, Madarász, J. X., additional, Marcellán, F., additional, Martini, H., additional, Mawhin, J., additional, McCoy, P. A., additional, McCune, W., additional, McGuire, G., additional, van der Mee, C. V. M., additional, Melville, D. J., additional, Michor, P. W., additional, Mihalik, M., additional, Moroşanu, C., additional, Morris, A. O., additional, Mulvey, C. J., additional, Muñoz, V., additional, Naimpally, S., additional, Narkiewicz, Władysław, additional, Nelsen, R. B., additional, Németi, I., additional, Neuman, F., additional, Newelski, L., additional, Niblo, G. A., additional, Nielsen, M. A., additional, Nistor, V., additional, Norberg, R., additional, Nowicki, T., additional, Oberguggenberger, M., additional, Olivari, D., additional, O’Neil, T. C., additional, Oonincx, P. J., additional, Ortiz, E. L., additional, Owen, G., additional, Pap, E., additional, Paulauskas, V., additional, Pearson, D. B., additional, Pedersen, G. K., additional, Pelz, R. B., additional, Petryshyn, W. V., additional, Philippou, A. N., additional, Pigozzi, D., additional, Pinkus, A., additional, Piotrowski, Z., additional, Pollack, R., additional, Prástaro, A., additional, Prékopa, András, additional, Przytycki, J., additional, Ramm, A. G., additional, Rassias, T. M., additional, Reich, S., additional, Reischuk, R., additional, Rodabaugh, S. E., additional, Palacios, A. Rodriguez, additional, Rosenberg, J., additional, Ruciński, A., additional, Sándor, J., additional, Schmid, P., additional, Schumacher, J. M., additional, Sehgal, S. K., additional, Shoikhet, D., additional, Silbermann, B., additional, Simson, D., additional, Sitaram, A., additional, de Snoo, H., additional, Soffer, A., additional, Sottile, F., additional, Spencer, J., additional, Srivastava, H. M., additional, Stegeman, J. D., additional, Stegenga, D., additional, Steinberg, R., additional, Stroeker, R. J., additional, Sumida, H., additional, Székely, Łászló A., additional, Todor, F., additional, Tsekanovskii, E., additional, Turull, A., additional, Tzanakis, N., additional, Unger, L., additional, Upmeier, H., additional, Varga, R. S., additional, Vasconcelos, W., additional, Vassiliou, P. J., additional, Vinnikov, V., additional, Vuorinen, M., additional, Waldschmidt, M., additional, Watt, N., additional, Wene, G. P., additional, Wiegerinck, J., additional, Wijsman, R. A., additional, Wittenberg, R. W., additional, Wolpert, S. A., additional, Xiang, S., additional, Zalcman, L., additional, Zayed, A. I., additional, Zlobec, S., additional, and Zucker, S., additional

Published
2002
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12. Analysis in functional spaces

Author

Bourgain, J., Pełczyński, A., Komarchev, I. A., Makarov, B. M., Wojtaszczyk, P., Casazza, P. G., Semënov, E. M., Jones, Peter W., Zahariuta, V. P., Semiguk, O. S., Skiba, N. I., Haslinger, F., Aizenberg, L. A., Trutnev, V. M., Havin, Victor P., editor, Hruščëv, Sergei V., editor, and Nikol'skii, Nikolai K., editor

Published
1984
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13. Geometric Generalizations in Kresin–Maz’ya Sharp Real-Part Theorems

Author

Aizenberg, L., Vidras, Alekos, and Vidras, Alekos [0000-0001-9917-8367]

Subjects
Computational Mathematics, Pure mathematics, Computational Theory and Mathematics, Applied Mathematics, Calculus, Real part theorems, Operator theory, Sharp constants, Mathematics
Abstract

In the present article we present some geometric generalizations of the estimates from Chapters 5,6,7 of the monograph [7]. © 2007 Birkhaeuser. 2 3 405 415

Published
2007
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14. Duality for Hardy Spaces in Domains of ℂn and Some Applications

Author

Aizenberg, L., Gotlib, V., Vidras, Alekos, and Vidras, Alekos [0000-0001-9917-8367]

Subjects
Duality, Dual complement
Abstract

Let Ω ⊂ ℂn be a bounded, strictly convex domain with C3 boundary and Ω̃ be its dual complement. We prove that (Hp(Ω))″ = Hp(Ω̃), where p > 1 and 1/p + 1/q = 1. As an application of the above results we give the precise description of the dual space of the space of holomorphic functions defined in a special type of domains Ω ⊂ ℂn and which are representable by Carleman integral representation formula. © 2013 Springer Basel. 8 6 1341 1366

Published
2014

26. On a class of holomorphic functions representable by Carleman formulas in the disk from their values on the arc of the circle

Author

Aizenberg, L., Vidras, Alekos, and Vidras, Alekos [0000-0001-9917-8367]

Subjects
Lebesgue measure, General Mathematics, Smirnov classes, Mathematical analysis, Holomorphic function, Function (mathematics), Characterization (mathematics), Identity theorem, Unit disk, Combinatorics, Arc (geometry), Unit circle, Carleman formula, Mathematics
Abstract

Let D be a unit disk and M be an open arc of the unit circle whose Lebesgue measure satisfies 0 < l(M) < 2π Our first result characterizes the restriction of the holomorphic functions f ∈ H(D), which are in the Hardy class H1 near the arc M and are denoted by N HM 1 (D), to the open arc M. This result is a direct consequence of the complete description of the space of holomorphic functions in the unit disk which are represented by the Carleman formulas on the open arc M. As an application of the above characterization, we present an extension theorem for a function f ∈ L1 (M) from any symmetric sub-arc L ⊂ M of the unit circle, such that L̄ ⊂ M, to a function f ∈ N H L1(D). © 2007 WILEY-VCH Verlag GmbH & Co. KGaA. 280 1-2 5 19 Cited By :2

Published
2007

27. Analysis in functional spaces

Author

Bourgain, J., primary, Pełczyński, A., additional, Komarchev, I. A., additional, Makarov, B. M., additional, Wojtaszczyk, P., additional, Casazza, P. G., additional, Semënov, E. M., additional, Jones, Peter W., additional, Zahariuta, V. P., additional, Semiguk, O. S., additional, Skiba, N. I., additional, Haslinger, F., additional, Aizenberg, L. A., additional, and Trutnev, V. M., additional

Published
1984
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30. On Carleman formulas and on the class of holomorphic functions representable by them

Author

Aizenberg, L., Vidras, Alekos, and Vidras, Alekos [0000-0001-9917-8367]

Subjects
Analytic continuation, Mathematics::Complex Variables, Carleman formulas, Mathematics::Analysis of PDEs
Abstract

Carleman formulas, unlike the Cauchy formula, restore a function holomorphic in a domain D by its values on a part M of the boundary ∂D, provided that M is of positive Lebesgue measure. An extensive survey of Carleman formulas is found in [AIZ]. In the present paper new Carleman formulas are obtained for domains in ℂn and the question about a description of the class of holomorphic functions that are represented by Carleman formula is investigated. In [AIZTV] we considered the simplest Carleman formulas in one and several complex variables on particular simply connected domains. It was shown there that a necessary and sufficient condition for a holomorphic function f to be represented by Carleman formula over the set M is that f must belong to "the Hardy class ℋ1 near the set M". In the present paper we look at the case of Fok-Kuni integral representation formula. This is a particular form of abstract Carleman formula, but it involves simply connected domains, not covered by previous results. Furthermore we initiate the study of the same questions for non-simply connected domains. We obtain the description of the class of functions representable by Carleman formula on annulii in ℂ and their generalizations, the Reinhardt domains in ℂn. 237 5 25 Cited By :5

Published
2002

31. On small complete sets of functions

Author

Aizenberg, L., Vidras, Alekos, and Vidras, Alekos [0000-0001-9917-8367]

Abstract

Using Local Residues and the Duality Principle a multidimensional variation of the completeness theorems by T. Carleman and A. F. Leontiev is proven for the space of holomorphic functions defined on a suitable open strip Tα C C2. The completeness theorem is a direct consequence of the Cauchy Residue Theorem in a torus. With suitable modifications the same result holds in Cn. 52 1 3 30

Published
2000

35. S

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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36. E

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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37. P

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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38. Z

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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39. W

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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40. V

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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41. T

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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42. R

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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43. Q

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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44. N

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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45. O

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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46. M

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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47. L

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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48. K

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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49. J

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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50. I

Author

Hazewinkel, M., Abhyankar, S. S., Abramov, V., Adem, A., Aizenberg, L., Albeverio, S., Alías, Luís J., Andréka, H., Apanasov, B. N., Assani, I., Atanassov, K., Axler, S., Bagchi, A., Balachandran, K., Bapat, R. B., Bardos, C., Bartsch, T., Bates, P. W., Belinsky, E. S., and Ben-Israel, A.

Published
2002
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