## Linear Operators: Spectral operators |

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Page 1918

... of Kato - Kuroda has a long history in physics : many elaborate calculations

have been based upon it , and it has even suggested a standpoint which certain

physicists have been willing to

.

... of Kato - Kuroda has a long history in physics : many elaborate calculations

have been based upon it , and it has even suggested a standpoint which certain

physicists have been willing to

**consider**as an axiomatic basis for quantum theory.

Page 2051

We next

Cauchy problem whose existence is established in Theorem 19 . As before , we

assume that at > 0 . It follows from equation ( 55 ) which gives the analytical ...

We next

**consider**the problem of finding the explicit form of the solu . tion to theCauchy problem whose existence is established in Theorem 19 . As before , we

assume that at > 0 . It follows from equation ( 55 ) which gives the analytical ...

Page 2409

( a ) Instead of

That is , instead of

space Lp ( D , X ) of all X - valued Borel - Lebesgue measurable functions

defined ...

( a ) Instead of

**considering**, as above , the space L2 ( D ) of complex valued ...That is , instead of

**considering**the space L2 ( D ) as above , we may**consider**thespace Lp ( D , X ) of all X - valued Borel - Lebesgue measurable functions

defined ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero