## Linear Operators: Spectral operators |

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Page 2021

For each s in R2 this matrix is normal and (23) A(s)A*(s) = \s\2I = A*(s)A(s), seR2,

so that

5i M, o#«e*» and (26) = M «eS,^6§2. The

For each s in R2 this matrix is normal and (23) A(s)A*(s) = \s\2I = A*(s)A(s), seR2,

so that

**Equation**(24) shows that \s\ ~ 1A(s) is unitary for s ^ 0. Thus (25) i-iW = Z!(5i M, o#«e*» and (26) = M «eS,^6§2. The

**equation**.4<p = 0, being equivalent to ...Page 2073

The first

second from the fact that they belong to the commutative algebra and

28) follows from (26). With each operator a in $li we associate an operator a + in

the ...

The first

**equation**in (27) follows from the definitions of the operators £(f±)> tnesecond from the fact that they belong to the commutative algebra and

**equation**(28) follows from (26). With each operator a in $li we associate an operator a + in

the ...

Page 2074

Now let y be an arbitrary vector in S>+ and define the vector x by the

). Then (31) shows that x is in Sj + and

some vector z in §_ we have eW-iy^e-'e-w+^x + z, and, using (30), it is seen that y

...

Now let y be an arbitrary vector in S>+ and define the vector x by the

**equation**(36). Then (31) shows that x is in Sj + and

**equation**(35) holds. This means that forsome vector z in §_ we have eW-iy^e-'e-w+^x + z, and, using (30), it is seen that y

...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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