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Functional Analysis: Entering Hilbert Space
Matematikkens Uendelige Univers
Emnerne i bogen er mangfoldige og strækker sig fra beskrivelse
af geometriske former og fænomener i omverdenen til diskussion
af nogle af uendelighedsbegrebets mange aspekter.
Store dele af bogen kræver ikke specielle matematiske forkundskaber,
men nok en vis optagethed af faget. Bogen giver i glimt
smagsprøver på matematikkens abstrakte idèverden, herunder
et indblik i nogle af matematikkens nyeste landvindinger.
Fundamental Concepts in Modern Analysis
This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof
of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the
space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm
in a space of continuous functions, including proofs of the basic inequalities of Hölder and Minkowski. The Lp-spaces
thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping the
main ideas more rapidly. Other important Banach spaces arising from function spaces and sequence spaces are also treated.
Denne bog henvender sig til alle der ønsker et indblik i matematikkens
mange bidrag til kultur, videnskab og samfund. Bogen er derfor tilrettelagt som en række små essays,
hvor der tilstræbes en mere beskrivende og fortællende fremstilling end normalt i bøger med et matematisk indhold.
Many advanced mathematical disciplines, such as dynamical systems, calculus of variations, differential geometry and
the theory of Lie groups, have a common foundation in general topology and calculus in normed vector spaces. In this book,
mathematically inclined engineering students are offered an opportunity to go into some depth with fundamental notions
from mathematical analysis that are not only important from a mathematical point of view but also occur frequently in
the more theoretical parts of the engineering sciences. The book should also appeal to university students in mathematics
and in the physical sciences.