Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 916
The sets en will be called the multiplicity sets of the ordered representation . ... with measures j and , and multiplicity sets { en } and { ēn } will be called equivalent if u ħ and u ( endèn ) = 0 ) = û ( endēm ) for n 1 , 2 , .
The sets en will be called the multiplicity sets of the ordered representation . ... with measures j and , and multiplicity sets { en } and { ēn } will be called equivalent if u ħ and u ( endèn ) = 0 ) = û ( endēm ) for n 1 , 2 , .
Page 1217
The sets e , will be called the multiplicity sets of the ordered representation . If plex ) > 0 and u ( x + 1 ) = 0 then the . ordered representation is said to have multiplicity k . If ulex ) > 0 for all k , the representation is said ...
The sets e , will be called the multiplicity sets of the ordered representation . If plex ) > 0 and u ( x + 1 ) = 0 then the . ordered representation is said to have multiplicity k . If ulex ) > 0 for all k , the representation is said ...
Page 1297
If Alf ) = 0 for each function in the domain of T , ( ) which vanishes in a neighborhood of a , A will be called a boundary value at a . The concept of a boundary value at b is defined similarly . By analogy with Definition XII.4.25 an ...
If Alf ) = 0 for each function in the domain of T , ( ) which vanishes in a neighborhood of a , A will be called a boundary value at a . The concept of a boundary value at b is defined similarly . By analogy with Definition XII.4.25 an ...
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additive adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero