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The Mathematical Apparatus for Quantum-Theories

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Cover of 'The Mathematical Apparatus for Quantum-Theories'

Table of Contents

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    Book Overview
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    Chapter 1 General tribes (Boolean lattices)
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    Chapter 2 Special theorems on Boolean Lattices
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    Chapter 3 Important auxiliaries
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    Chapter 4 General theory of traces
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    Chapter 5 The tribe of figures on the plane
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    Chapter 6 The trace-theorem
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    Chapter 7 The lattice of subspaces of the Hilbert-Hermite space
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    Chapter 8 Tribes of spaces
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    Chapter 9 Double scale of spaces
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    Chapter 10 Linear operators permutable with a projector
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    Chapter 11 Some double Stieltjes’ and Radons integrals
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    Chapter 12 Maximal normal operator and its canonical representation
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    Chapter 13 Operators $$N{f^ \cdot }\left( {\mathop {{\text{ }}x}\limits^ \cdot } \right){ = _{df}}\varphi \left( x \right) \cdot \mathop {{\text{ }}f}\limits^ \cdot \left( {\mathop {{\text{ }}x}\limits^ \cdot } \right)$$ for ordinary functions f
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    Chapter 14 Operational calculus on general maximal normal operators
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    Chapter 15 Theorems on normal operators and on related canonical mapping
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    Chapter 16 Some classical theorems on normal and selfadjoint operators
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    Chapter 17 Multiplicity of spectrum of maximal normal operators
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    Chapter 18 On items of operational calculus with application to the resolvent and spectrum of normal operators
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    Chapter 19 Tribe of repartition of functions
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    Chapter 20 Permutable normal operators
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    Chapter 21 Approximation of somata by complexes
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    Chapter 22 Vector fields on the tribe and their summation
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    Chapter 23 Quasi-vectors and their summation
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    Chapter 24 Summation of quasi-vectors in the separable and complete Hilbert-Hermite space
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    Chapter 25 General orthogonal systems of coordinates in the separable and complete Hilbert-Hermite-space
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    Chapter 26 Dirac’s Delta-function
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    Chapter 27 Auxiliaries for a deeper study of summation of scalar fields
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    Chapter 28 Upper and lower (DARS)-summation of fields of real numbers in a Boolean tribe in the absence of atoms
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    Chapter 29 Upper and lower summation in the general case. Complete admissibility. Square summability of fields of numbers
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Title
The Mathematical Apparatus for Quantum-Theories
Published by
Springer Berlin Heidelberg, December 2012
DOI 10.1007/978-3-642-46030-2
ISBNs
978-3-64-246032-6, 978-3-64-246030-2
Authors

Nikodým, Otton Martin