Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 1298
First of all , it is clear from the preceding definition that the set M. ( the set M , ) of boundary values at a ( at b ) is a subspace of the space M of all boundary values . Let fi and fa be two functions in C® ( 1 ) such that fı ( t ) ...
First of all , it is clear from the preceding definition that the set M. ( the set M , ) of boundary values at a ( at b ) is a subspace of the space M of all boundary values . Let fi and fa be two functions in C® ( 1 ) such that fı ( t ) ...
Page 1373
Clearly , if V is as in Theorem 13 ( i ) , û = AV . It is clear from the definition of A that for each n - tuple F [ 1 , ... , In ] of Borel functions defined on 1 , AF € L2 ( 1 , { ôi ; } ) if and only if FeL2 ( 4 , { p } ) .
Clearly , if V is as in Theorem 13 ( i ) , û = AV . It is clear from the definition of A that for each n - tuple F [ 1 , ... , In ] of Borel functions defined on 1 , AF € L2 ( 1 , { ôi ; } ) if and only if FeL2 ( 4 , { p } ) .
Page 1689
Indeed , if { Am } is a Cauchy sequence in L ( 1 ) , it is clear from ( i ) that { 2+ { m } is a Cauchy sequence in L ( I ) for IJ Sk , so that there exist functions g , gol in L , ( I ) such that limm - com - glp = 0 and limm - c1011m ...
Indeed , if { Am } is a Cauchy sequence in L ( 1 ) , it is clear from ( i ) that { 2+ { m } is a Cauchy sequence in L ( I ) for IJ Sk , so that there exist functions g , gol in L , ( I ) such that limm - com - glp = 0 and limm - c1011m ...
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