Πλειογραμμικές Απεικονίσεις σε χώρους Banach. Πολυώνυμα επιτυγχάνοντα νόρμα σε χώρους Banach και ειδικά σε χώρους Hilbert. Γενίκευση της ανισότητας του Hilbert.

Αλέξανδρος Παππάς

Abstract


Μελετάμε  τέσσερις κατηγορίες προβλημάτων. Πολυώνυμα επιτυγχάνοντα νόρμα σε χώρους Banach και ειδικά σε χώρους  Hilbert. Υπολογισμός της νόρμας πολυωνύμων πεπερασμένου τύπου. Τελεστές Hankel σε χώρους Hilbert. Γενίκευση της ανισότητας του Hilbert.


References


V. Anagnostopoulos and SZ. Gy. Révész, (2003). Polarization constants for products of linear functional over and and Chebyshev constants of the unit sphere. Preprint of the Alfréd Rényi Mathematical Institute, Hung. Acad. Sci., (4) 9 p.

J. Arias-de-Reyna, (1998). Gaussian Variables, Polynomials and Permanents. Linear Algebra and Appl. (285) 395-408.

K. M. Ball, (2001). The Complex Plank Problem, Bull. London Math. Soc., (33) 433-442.

K. M. Ball, (1991). The Plank Problem for Symmetric Bodies, Invent. math., (104) 535-543.

S. Banach, (1938). Über Homogene Polynome in , Studia Math., (7) 36-44.

T. Bang, (1951). A solution of the plank problem. Proc. Amer. Math. Soc., (2) 990-993.

B. Beauzamy, E. Bombieri, P. Enflo and H. L. Montgomery, (1990). Products of Polynomials in Many Variables. J. Number Theory, (36).

C. Benitez and Y. Sarantopoulos, (1993). Characterization of Real Inner Product Spaces by Means of Symmetric Bilinear Forms, J. Math. Anal. Appl, (180) 207-220.

C. Benitez, Y. Sarantopoulos and A.Tonge, (1998). Lower Bounds for Norms of Products of Polynomials, Math. Proc. Camb. Phil. Soc., (124) 395-408.

J. Bochnak and J. Siciak, (1971). Polynomials and multilinear mappings in topological vector spaces, Studia Math., (39) 59-76.

S. B. Chae, (1985). Holomorphy and calculus in normed spaces, Marcel Dekker.

S. Dineen, (1999). Complex Analysis on Infinite Dimensional Spaces, Springer Monographs in Mathematics, Springer-Verlag, Berlin.

P. L. Duren, (1970). Theory of Spaces, Academic Press.

J. C. García-Vázquez and R. Villa, (1999). Lower bounds for multilinear forms defined on Hilbert spaces, Mathematika, (46) 315-322.

L. A. Harris, (1975). Bounds on the derivatives of holomorphic functions of vectors, in: Colloque d'Analyse (Rio de Janeiro, 1972), L. Nachbin ed Actualités Sci. Indust. 1367, Hermann, Paris, 145-163.

H. Helson, (1983). Harmonic Analysis, Addison--Wesley.

Hörmander, (1954). On a Theorem of Grace, Math. Scand., (2) 55-64.

Y. Katznelson, (1968). An Introduction to Harmonic Analysis, Dover.

O. D. Kellog, (1928). On Bounded Polynomials in Several Variables, Math. Zeit, (279) 55-64.

P. Kirwan, Y. Sarantopoulos and A. M. Tonge, (1999). Extremal homogeneous polynomials on real normed spaces, J. Approx. Theory, (97) 201-213.

A. Kroό and I. Pritsker, (1999). A Sharp Version of Mahler's Inequality for Products of Polynomials, Bull. London Math. Soc., (31).

A. E. Litvak, V. D. Milman and G. Schechctman, (1998). Averages of norms and quasi-norms, Math. Ann., (312) 95-124.

K. Mahler, (1960). An Application of Jensen's Formula to Polynomials, Mathematika, (7) 98-100.

A. M. Mantero and A.M. Tonge, (1979). Banach algebras and Neumann's inequality, J. London Math. Soc., (38) 309-334, (1979).

A. M. Mantero and A.M. Tonge, (1979). The Schur multiplication in tensor algebras, Studia Math., (68) 1-24.

I. Masri and A.M. Tonge, (2005). Norm estimates for random multilinear Hankel forms, Linear Algebra Appl., (402) 255-262.

M. Matolcsi, (2005). The th linear polarization constant of , Acta Math. Hung., (108) 127-134.

M. Matolcsi, (2005). A geometric estimate on the norm of product of functionals, Linear Algebra Appl., (405) 304-310.

G. Munoz, Y. Sarantopoulos and A. Tonge, (1999). Complexifications of Real Banach Spaces, Polynomials and Multilinear Maps, Studia Math., (134) 1-33.

Z. Nehari, (1957). On bounded bilinear forms. Ann. of Math., (65) 153-162.

A. Pappas and Sz. Gy. Révész, (2004). Linear polarization constants of Hilbert spaces. Journal Mathematical Analysis and Applications, (300) 129-146.

A. Pappas, (2005). Πλειογραμμικές απεικονίσεις και πολυώνυμα σε χώρους Banach (διδακτορική διατριβή). Ε.Μ.Πολυτεχνείο.

A. Pappas, Y. Sarantopoulos and A. Tonge, (2007). Norm attaining polynomials. Bulletin of the London Mathematical Society. (10) (255-264)

A. Pappas, Y. Sarantopoulos and A. Tonge, (2008). Generalizations of Hardy-Hilbert's inequality.

J.R. Partington, (1988). An introduction to Hankel operators, Cambridge University Press.

J.C. Power, (1982). Hankel operators on Hilbert space, Pitman.

Sz. Gy. Révész and Y. Sarantopoulos, (2004). Plank problems, polarization, and Chebyshev constants, J. Korean Math. Soc., 157-174.

R. Ryan and B. Turett, (1998). Geometry of Spaces of Polynomials, J. of Math. Anal. Appl., (221) 698-711.

Y. Sarantopoulos, (1987). Extremal multilinear forms on Banach spaces, Proc. Amer. Math. Soc., (99) 340-346.

A. E. Taylor, (1938). Additions to the theory of polynomials in normed linear spaces, Tôhoku Math. J., (44) 302-318.

N. Varopoulos, (1974). On an inequality of von Neumann and an application of the metric theory of tensor products to operator theory, J. Funct. Anal., (16) 83-100.


Refbacks

  • There are currently no refbacks.