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Page 1280
A formal differential operator of order n on the interval I is an expression din - 1 T = an ( t ) din tan - 1 ( t ) dt ( ) + ... + ao ( t ) , dt , n d - Σα , ( t ) ( ) dt i = 0 > such that the complex - valued functions aí , called the ...
A formal differential operator of order n on the interval I is an expression din - 1 T = an ( t ) din tan - 1 ( t ) dt ( ) + ... + ao ( t ) , dt , n d - Σα , ( t ) ( ) dt i = 0 > such that the complex - valued functions aí , called the ...
Page 1289
Thus c ; ( t ) = a ; ( t ) which shows that ( T * ) * = T. Q.E.D. A number of other principles belonging to the formal algebra of formal differential operators are worth mentioning although we shall not make much use of them ; for this ...
Thus c ; ( t ) = a ; ( t ) which shows that ( T * ) * = T. Q.E.D. A number of other principles belonging to the formal algebra of formal differential operators are worth mentioning although we shall not make much use of them ; for this ...
Page 1290
that since time ( 1271 ) * , the operator n i 31-10 ( Σ ( -1 ) : ( ( ) p . ( t ) dt n is formally self adjoint provided only that the coefficients pi are real . In the same way , the formal differential operator ( 1/2 ) ( d / dt ) " { p ...
that since time ( 1271 ) * , the operator n i 31-10 ( Σ ( -1 ) : ( ( ) p . ( t ) dt n is formally self adjoint provided only that the coefficients pi are real . In the same way , the formal differential operator ( 1/2 ) ( d / dt ) " { p ...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero