## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 1983

... A of all convolution operators in H = L ( RN ) , the Hilbert space of

ordinary Lebesgue integrals , proper value integrals or any other improper

integral , is ...

... A of all convolution operators in H = L ( RN ) , the Hilbert space of

**square****integrable**functions on real Euclidean space ... countably additive set functions ,ordinary Lebesgue integrals , proper value integrals or any other improper

integral , is ...

Page 2042

1 ) we have , by differentiating under the integral sign as before , ( To co » ) ( q ) =

$ . v ( – 191 « la ga ( F - 14163393° ( 8 ) ... it follows that the coefficient of y ( s ) in

the preceding integrand is

1 ) we have , by differentiating under the integral sign as before , ( To co » ) ( q ) =

$ . v ( – 191 « la ga ( F - 14163393° ( 8 ) ... it follows that the coefficient of y ( s ) in

the preceding integrand is

**square integrable**on RN and the same is true of its ...Page 2332

If « = iß is purely imaginary , then we decompose f into a finite sum of

and immediately apply the ordinary theory of orthogonal expansions in Hilbert

space ...

If « = iß is purely imaginary , then we decompose f into a finite sum of

**square****integrable**functions , each vanishing outside an interval of length at most 1 / 8 ,and immediately apply the ordinary theory of orthogonal expansions in Hilbert

space ...

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