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Spektraldarstellung Linearer Transformationen des Hilbertschen Raumes

Spektraldarstellung Linearer Transformationen des Hilbertschen Raumes

Bela von Szeged Nagy

73,07 €
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Editorial:
Springer Nature B.V.
Año de edición:
1941
Materia
Física
ISBN:
9783642983542
73,07 €
IVA incluido
Disponible

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Sobre IBD

In seinen Untersuchungen iiber Integralgleichungen wurde HILBERT zum Begriff des unendlichen Folgenraumes .fJ gefiihrt. Die Elemente von .fJ sind die 'Vektoren' a mit unendlichvielen Komponenten (aI’ a , . . .) und von endlicher Norm II a II = [i a] t; das inn ere Pro- 2 z k~l 00 dukt (0, 0) der Vektoren a und 0 wird dann durch ~ akbk definiert. k~l Die Geometrie dieses Raumes hat viele Analogien zur Geometrie eines endlichdimensionalen Vektorraumes, es treten aber beim Ubergang vom endlich- zum unendlichdimensionalen freilich auch neue Erschei­ nungen auf. 1st A eine lineare Transformation des n-dimensionalen Vektor­ raumes ffi', deren Matrix symmetrisch ist, so weiB man z. B., daB es paarweise orthogonale Einheitsvektoren aI’ a , .•. , Un und reelle Zah­ 2 len AI’ A , •.• , An (Ak

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