## Linear Operators, Part 1 |

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Page 32

The

of topological spaces . Then the product topology is the topology t in X = P_X_

obtained by taking the collection of all sets U = P.U. , where each U , is open ,

and ...

The

**formal**definition follows : 1 DEFINITION . Let ( Xą , tą ) be an indexed familyof topological spaces . Then the product topology is the topology t in X = P_X_

obtained by taking the collection of all sets U = P.U. , where each U , is open ,

and ...

Page 90

... ( x1 + x , ) y = xy + x , y , ap ( x ® y ) = ( ax ) * ( By ) This can be attained by

taking the set X o Y of all finite

Such a space is called the direct product ( although the terms tensor , cross , and

...

... ( x1 + x , ) y = xy + x , y , ap ( x ® y ) = ( ax ) * ( By ) This can be attained by

taking the set X o Y of all finite

**formal**sums Xx ; Yi with suitable identifications .Such a space is called the direct product ( although the terms tensor , cross , and

...

Page 359

( v ) e - inx dx is called the nth Fourier coefficient of 1 and the

1/2 Eineint is called the Fourier series of f . 13 Show that if { en } is a sequence

with colcn | 2 < oo , then there is some f in L , whose nth Fourier coefficient is Cn ...

( v ) e - inx dx is called the nth Fourier coefficient of 1 and the

**formal**series ( 27 ) -1/2 Eineint is called the Fourier series of f . 13 Show that if { en } is a sequence

with colcn | 2 < oo , then there is some f in L , whose nth Fourier coefficient is Cn ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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