The boundary behaviour of $S_p$-valued functions analytic in the half-plane with nonnegative imaginary part

• Autorzy: S. N. Naboko
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1994
• Tom: 30
• Numer: 1
• Strony: 277-285

Daty

wydano

1994

Twórcy

autor

S. N. Naboko

• Department of Mathematical Physics, Faculty of Physics, St. Petersburg University, St. Petersgoff, Ulyanovskaya 1, 198904 St. Petersburg, Russia

Bibliografia

• [1] K. Asano, Notes on Hilbert transforms of vector valued functions in the complex plane and their boundary values, Publ. Res. Inst. Math. Sci. 13 (1967), 572-577.
• [2] F. V. Atkinson, Discrete and Continuous Boundary Value Problems, Russian edition, Mir, Moscow, 1968 (additional chapters devoted to R-functions written by M. G. Kreĭn and I. Kats).
• [3] M. S. Birman and S. B. Entina, A stationary approach to abstract scattering theory, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 401-430 (in Russian); English transl. in Math. USSR-Izv. 1 (1967).
• [4] M. S. Birman and D. R. Yafaev, Spectral properties of the scattering matrix, Algebra i Analiz 4 (6) (1992), 1-27 (in Russian).
• [5] J. Bourgain, Vector valued singular integrals and the H¹-BMO duality, Israel Sem. Geom. Aspects Funct. Anal. (1983/84), XVI, Tel Aviv Univ., 1984, 23 pp.
• [6] J. Bourgain and W. J. Davis, Martingale transforms and complex uniform convexity, Trans. Amer. Math. Soc. 294 (1986), 501-515.
• [7] A. V. Bukhvalov, Continuity of operators acting in spaces of vector-valued functions, applications to the theory of bases, Zap. Nauchn. Sem. LOMI 157 (1987), 5-22 (in Russian).
• [8] D. L. Burkholder, Martingale transforms and the geometry of Banach space, in: Lecture Notes in Math. 860, Springer, 1981, 35-50.
• [9] D. L. Burkholder, A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions, in: Conf. Harmonic Anal. in Honor of A. Zygmund (Chicago, 1981), Wadsworth, Belmont, Calif., 1983, 270-286.
• [10] L. D. Faddeev, On the Friedrichs model in the theory of perturbations of the continuous spectrum, Trudy Mat. Inst. Steklov. 73 (1964), 292-313 (in Russian); English transl. in Amer. Math. Soc. Transl. (2) 62 (1967).
• [11] I. Ts. Gokhberg and M. G. Kreĭn, Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space, Amer. Math. Soc., Providence, R.I., 1969.
• [12] I. Ts. Gokhberg and M. G. Kreĭn, The Theory of Volterra Operators in a Hilbert Space, Amer. Math. Soc., Providence, R.I., 1970.
• [13] J. A. Gutierrez and H. E. Lacey, On the Hilbert transform for Banach valued functions, in: Lecture Notes in Math. 939, Springer, 1982, 73-80.
• [14] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966.
• [15] P. Koosis, Introduction to $H^p$-Spaces, Cambridge Univ. Press, 1980.
• [16] V. I. Matsaev and Yu. A. Palant, On the powers of a bounded dissipative operator, Ukrain. Mat. Zh. 14 (1962), 329-337 (in Russian).
• [17] S. N. Naboko, A functional model of perturbation theory and its applications in scattering theory, Trudy Mat. Inst. Steklov. 147 (1980), 84-114 (in Russian); English transl. in Proc. Steklov Inst. Math. 1981, (2).
• [18] S. N. Naboko, On conditions for the existence of the wave operators in the nonselfadjoint case, in: Probl. Mat. Fiz. 12, Leningrad Univ., 1987, 132-155 (in Russian).
• [19] S. N. Naboko, On the boundary values of analytic operator-valued functions with positive imaginary part, Zap. Nauchn. Sem. LOMI 157 (1987), 55-69 (in Russian).
• [20] S. N. Naboko, Uniqueness theorems for operator-valued functions with positive imaginary part and the singular spectrum in the selfadjoint Friedrichs model, Ark. Mat. 25 (1987), 115-140.
• [21] S. N. Naboko, Nontangential boundary values of operator-valued R-functions in a half-plane, Algebra i Analiz 1 (5) (1989), 197-222 (in Russian); English transl.: Leningrad Math. J. 1 (5) (1990), 1255-1278.
• [22] B. S. Pavlov and L. D. Faddeev, Zero sets of operator functions with a positive imaginary part, in: Lecture Notes in Math. 1043, Springer, 1984, 124-128.
• [23] B. S. Pavlov and S. V. Petras, On the singular spectrum of a weakly perturbed multiplication operator, Funktsional. Anal. i Prilozhen. 4 (2) (1970), 54-61 (in Russian); English transl. in Functional Anal. Appl. 4 (1970).
• [24] J. L. Rubio de Francia, Fourier series and Hilbert transforms with values in UMD Banach spaces, Studia Math. 81 (1985), 95-105.
• [25] R. Ryan, Boundary values of analytic vector valued functions, Proc. Nederl. Akad. Wetensch. Ser. A 65 (1962), 558-572.
• [26] J. Schwartz, A remark on inequalities of Calderón-Zygmund type for vector-valued functions, Comm. Pure Appl. Math. 14 (1961), 785-799.
• [27] E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.
• [28] B. Sz.-Nagy and C. Foiaş, Analyse Harmonique des Opérateurs de l'Espace de Hilbert, Masson, Paris, 1967.
• [29] V. F. Veselov and S. N. Naboko, The determinant of a characteristic function and the singular spectrum of a nonselfadjoint operator, Mat. Sb. 129 (171) (1986), 20-29 (in Russian); English transl. in Math. USSR-Sb. 57 (1987).