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Haar Series and Linear Operators
In 1909 Alfred Haar introduced into analysis a remarkable system which bears his name. The Haar system is a complete orthonormal system on [0,1] and the Fourier-Haar series for arbitrary continuous function converges uniformly to this function.
This volume is devoted to the investigation of the Haar system from the operator theory point of view. The main subjects treated classical results on unconditional convergence of the Haar series in modern presentation; Fourier-Haar coefficients; reproducibility; martingales; monotone bases in rearrangement invariant spaces; rearrangements and multipliers with respect to the Haar system; subspaces generated by subsequences of the Haar system; the criterion of equivalence of the Haar and Franklin systems.
This book will be of interest to graduate students and researchers whose work involves functional analysis and operator theory.
This volume is devoted to the investigation of the Haar system from the operator theory point of view. The main subjects treated classical results on unconditional convergence of the Haar series in modern presentation; Fourier-Haar coefficients; reproducibility; martingales; monotone bases in rearrangement invariant spaces; rearrangements and multipliers with respect to the Haar system; subspaces generated by subsequences of the Haar system; the criterion of equivalence of the Haar and Franklin systems.
This book will be of interest to graduate students and researchers whose work involves functional analysis and operator theory.
239 pages, Hardcover
First published January 31, 1997
About the author
Igor D. Novikov
19 books6 followersIgor Dmitriyevich Novikov (Russian: И́горь Дми́триевич Но́виков) is a Russian (and former Soviet) theoretical astrophysicist and cosmologist.
Novikov put forward the idea of white holes in 1964. He also formulated the Novikov self-consistency principle in the mid-1980s, a contribution to the theory of time travel.
Novikov gained his Ph.D. degree in astrophysics in 1965 and the Russian D.Sc. degree in astrophysics in 1970. From 1974 to 1990 he was head of the Department of Relativistic Astrophysics at the Russian Space Research Institute in Moscow. Before 1991 he was head of the Department of Theoretical Astrophysics at the Lebedev Physical Institute in Moscow and has been professor at Moscow State University. Since 1994 he has been director of the Theoretical Astrophysics Center (TAC) of the University of Copenhagen, Denmark. He is currently also a professor of astrophysics at the Observatory of the University of Copenhagen, where he has been since 1991. Since 1998 he has been a Fellow of the Royal Astronomical Society.
Novikov put forward the idea of white holes in 1964. He also formulated the Novikov self-consistency principle in the mid-1980s, a contribution to the theory of time travel.
Novikov gained his Ph.D. degree in astrophysics in 1965 and the Russian D.Sc. degree in astrophysics in 1970. From 1974 to 1990 he was head of the Department of Relativistic Astrophysics at the Russian Space Research Institute in Moscow. Before 1991 he was head of the Department of Theoretical Astrophysics at the Lebedev Physical Institute in Moscow and has been professor at Moscow State University. Since 1994 he has been director of the Theoretical Astrophysics Center (TAC) of the University of Copenhagen, Denmark. He is currently also a professor of astrophysics at the Observatory of the University of Copenhagen, where he has been since 1991. Since 1998 he has been a Fellow of the Royal Astronomical Society.
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