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The theme of this work, the logarithmic integral, lies athwart much
of twentieth-century analysis. It is a thread connecting many
apparently separate parts of the subject, and so is a natural point
at which to begin a serious study of real and complex analysis.
Professor Koosis' aim is to show how, from simple ideas, one can
build up an investigation which explains and clarifies many
different, seemingly unrelated problems; to show, in effect, how
mathematics grows. The presentation is straightforward, so that by
following the theme, Professor Koosis has produced a work that can
be read as a whole. He has brought together here many results, some
unpublished, some new, and some available only in inaccessible
journals.
The first edition of this well known book was noted for its clear
and accessible exposition of the basic theory of Hardy spaces from
the concrete point of view (in the unit circle and the half plane).
The intention was to give the reader, assumed to know basic real
and complex variable theory and a little functional analysis, a
secure foothold in the basic theory, and to understand its
applications in other areas. For this reason, emphasis is placed on
methods and the ideas behind them rather than on the accumulation
of as many results as possible. The second edition retains that
intention, but the coverage has been extended. The author has
included two appendices by V. P. Havin, on Peter Jones'
interpolation formula, and Havin's own proof of the weak sequential
completeness of L1/H1(0); in addition, numerous amendments,
additions and corrections have been made throughout.
The first edition of this book provided accessible exposition of
the basic theory of Hardy spaces from the concrete point of view
(in the unit circle and the half plane). The intention was to give
the reader, assumed to know basic real and complex variable theory
and a little functional analysis, a secure foothold in the basic
theory, and to understand its applications in other areas. For this
reason, emphasis is placed on methods and the ideas behind them
rather than on the accumulation of as many results as possible.
Computations are done in detail and there are many diagrams. The
second edition retains that intention, but the coverage has been
extended. The author has included two appendices by V. P. Havin, on
Peter Jones' interpolation formula, and Havin's own proof of the
weak sequential completeness of L1/H1(0); in addition, numerous
amendments, additions and corrections have been made throughout.
The theme of this unique work, the logarithmic integral, lies
athwart much of twentieth century analysis. It is a thread
connecting many apparently separate parts of the subject, and is a
natural point at which to begin a serious study of real and complex
analysis. Professor Koosis' aim is to show how, from simple ideas,
one can build up an investigation that explains and clarifies many
different, seemingly unrelated problems; to show, in effect, how
mathematics grows. The presentation is straightforward, so this,
the first of two volumes, is self-contained, but more importantly,
by following the theme, Professor Koosis has produced a work that
can be read as a whole. He has brought together here many results,
some new and unpublished, making this a key reference for graduate
students and researchers.
The theme of this work, the logarithmic integral, lies athwart much
of twentieth-century analysis. It is a thread connecting many
apparently separate parts of the subject, and so is a natural point
at which to begin a serious study of real and complex analysis.
Professor Koosis' aim is to show how, from simple ideas, one can
build up an investigation which explains and clarifies many
different, seemingly unrelated problems; to show, in effect, how
mathematics grows. The presentation is straightforward, so that by
following the theme, Professor Koosis has produced a work that can
be read as a whole. He has brought together here many results, some
unpublished, some new, and some available only in inaccessible
journals.
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R1,150
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Discovery Miles 8 890
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