## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1241

**Consequently**there is a number M such that lzml + SM , 1 , 2 , .... Moreover , given a > 0 there is an integer N such that if m , n > N , then 12m - 2-1 + < E. Thus ( 12,1+ ) 2 = | ( 2,2m ) + 1 + 1 ( 2m , 2 , -2m ) + 5 ( zn , 2m ) + I + ...Page 1383

With boundary conditions A , the eigenvalues are

With boundary conditions A , the eigenvalues are

**consequently**to be determined from the equation sin vă = 0 .**Consequently**, in Case A , the eigenvalues a are the numbers of the form ( Na ) , n 2 1 ; in Case C , the numbers { ( n + ] ...Page 1387

**Consequently**, by Theorem 3.16 , the resolvent R ( 2 ; T ) is an integral operator with the kernel sin Vās ( cos Vāt + i sin Vāt ) s < t , Ia > 0 , v t < s , 12 > 0 , sin Vāt ( cos Vīsti sin Văs ) v sin Văs ( cos vă - i sin Vāt ) va sin ...### What people are saying - Write a review

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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