## Linear Operators: Spectral operators |

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Page 2325

It also follows, from Lemma 3.5, formula (16), and formula (14), that the zero of M{

fi) in RTM has the

the

It also follows, from Lemma 3.5, formula (16), and formula (14), that the zero of M{

fi) in RTM has the

**asymptotic**representation and that the zero of M(jx) in Rf* hasthe

**asymptotic**representation where the £m and £m are certain coefficients.Page 2384

Q.E.D. For the spectral analysis of the operator T, we shall also need

information on the "second solution" of the differential equation to = tt2cr, that is,

the solution

...

Q.E.D. For the spectral analysis of the operator T, we shall also need

**asymptotic**information on the "second solution" of the differential equation to = tt2cr, that is,

the solution

**asymptotic**to e-1"' as <->oo. Since, in contrast to olt such a solution is...

Page 2394

... On the other hand, since these two solutions are linearly independent, we must

have a linear relation ct2 = ad1 + oct^ It is clear from Lemma 1 that such a linear

combination can only have the indicated

... On the other hand, since these two solutions are linearly independent, we must

have a linear relation ct2 = ad1 + oct^ It is clear from Lemma 1 that such a linear

combination can only have the indicated

**asymptotic**form if a = 1, b = c(fi(X)).### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectra Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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