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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
1. Introduction.......................................................................................................5
2. Basic definitions, notations and facts................................................................6
3. Definitions of the Genchev transform................................................................8
4. Basic properties of the Genchev transform......................................................11
5. Some properties of the weight $w_B$..............................................................16
6. The Bergman function of a tube domain..........................................................22
7. The Bergman space on a convex tube.............................................................26
8. On L²-holomorphic continuation of a function from the Bergman space...........31
9. L²-angles between multidimensional tubes.......................................................39
10. Calculations of some L²-angles between tube domains..................................58
References...........................................................................................................63
1. Introduction.......................................................................................................5
2. Basic definitions, notations and facts................................................................6
3. Definitions of the Genchev transform................................................................8
4. Basic properties of the Genchev transform......................................................11
5. Some properties of the weight $w_B$..............................................................16
6. The Bergman function of a tube domain..........................................................22
7. The Bergman space on a convex tube.............................................................26
8. On L²-holomorphic continuation of a function from the Bergman space...........31
9. L²-angles between multidimensional tubes.......................................................39
10. Calculations of some L²-angles between tube domains..................................58
References...........................................................................................................63
Słowa kluczowe
Tematy
Kategoryzacja MSC:
- 32A07: Special domains (Reinhardt, Hartogs, circular, tube)
- 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
- 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
- 32A25: Integral representations; canonical kernels (Szeg\H o, Bergman, etc.)
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
360
Liczba stron
64
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLX
Daty
wydano
1996
otrzymano
1994-06-27
poprawiono
1995-05-25
Twórcy
autor
- Department of Applied Mathematics, Warsaw Agricultural University, Nowoursynowska 166, 02-787 Warszawa, Poland
Bibliografia
- [1] N. I. Achiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, vols. 1, 2, Vysshaya Skhola, Kharkov, 1977, 1978 (in Russian); English transl.: Pitman Monographs Stud. Math. 9, 10, Pitman, Boston, 1981.
- [2] S. Bergman, The Kernel Function and Conformal Mapping, 2nd ed., Math. Surveys 5, Amer. Math. Soc., Providence, R.I., 1970.
- [3] S. Bochner and W. T. Martin, Several Complex Variables, Princeton Univ. Press, Princeton, N.J., 1948.
- [4] M. M. Dzhrbashyan and V. M. Martirosyan, Integral representations for some classes of functions holomorphic in a strip or in a halfplane, Anal. Math. 12 (1986), 191-212.
- [5] T. G. Genchev, Paley-Wiener type theorems for functions holomorphic in a half-plane, C. R. Acad. Bulgare Sci. 37 (1983), 141-144.
- [6] T. G. Genchev, Integral representations for functions holomorphic in tube domains, ibid. 37 (1984), 717-720.
- [7] I. S. Gradshteĭn and I. M. Ryzhik, Tables of Integrals, Sums, Series and Products, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1962 (in Russian); English transl.: Academic Press, New York, 1965.
- [8] W. Hyb, On the spectral properties of translation operators in one-dimensional tubes, Ann. Polon. Math. 55 (1991), 157-161.
- [9] W. Hyb, The Bergman function of the tube over an open ball, in: Classical Analysis, Proc. 6th Internat. Sympos., September 1991, T. Mazur (ed.), World Scientific, 1992, 17-28.
- [10] W. Hyb, Spectral properties of some holomorphic dynamical systems, Bull. Soc. Sci. Lettres Łódź 45, Sér. Rech. Déform. 19 (1995), 21-33.
- [11] A. D. Ioffe and V. M. Tikhomirov, Theory of Extremum Problems, Nauka, Moscow, 1974 (in Russian).
- [12] P. Jakóbczak, The stability of the L²-angles for plane domains, Simon Stevin 66 (1992), 257-294.
- [13] P. Jakóbczak, The stability of the L²-angle for increasing sequences of domains, Complex Variables Theory Appl. 22 (1993), 1-10.
- [14] P. Jakóbczak and T. Mazur, On discontinuity of L²-angle, J. Austral. Math. Soc. Ser. A 47 (1989), 269-279.
- [15] P. Jakóbczak and T. Mazur, Some properties of the L²-angle between complex domains, Rad. Mat. 7 (1991), 109-121.
- [16] S. Krantz, Function Theory of Several Complex Variables, Wiley, 1982.
- [17] I. P. Ramadanow and M. L. Skwarczyński, An angle in L² (ℂ) determined by two plane domains, Bull. Polish Acad. Sci. 32 (1984), 653-659.
- [18] R. T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, N.J., 1970.
- [19] M. Ruta, About some characterization of points of thinness for open set in the proof of Havin's approximation theorem, in: Classical Analysis, Proc. 6th Internat. Sympos., September 1991, T. Mazur (ed.), World Scientific, 1992, 227-232.
- [20] G. Rządkowski, On an angle between two rings, Bull. Austral. Math. Soc. 43 (1991), 79-87.
- [21] G. Rządkowski, An L²-angle between plane sectors, Demonstratio Math. 26 (1993), 33-45.
- [22] S. Saitoh, Integral transforms in Hilbert spaces, Proc. Japan Acad. Ser. A. Math. Sci. 58 (1982), 361-364.
- [23] S. Saitoh, Fourier-Laplace transforms and the Bergman spaces, Proc. Amer. Math. Soc. 102 (1988), 985-992.
- [24] L. Schwartz, Analyse Mathématique, vol. 1, Hermann, Paris, 1967.
- [25] M. Skwarczyński, Biholomorphic invariants related to the Bergman functions, Dissertationes Math. 173 (1980).
- [26] M. Skwarczyński, A general description of the Bergman projection, Ann. Polon. Math. 46 (1985), 311-315.
- [27] M. Skwarczyński, Alternating projections between a strip and a halfplane, Math. Proc. Cambridge Philos. Soc. 102 (1987), 121-129.
- [28] M. Skwarczyński, L²-Angles between one-dimensional tubes, Studia Math. 90 (1988), 213-233.
- [29] M. Skwarczyński, The punctured plane: alternating projections and L²-angles, Ann. Polon. Math. 52 (1991), 293-301.
- [30] E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971.
Języki publikacji
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Uwagi
1991 Mathematics Subject Classification: 32H10, 42B10, 32A07, 46E22.
Identyfikator YADDA
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Identyfikatory
ISSN
0012-3862
Kolekcja
DML-PL
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