The Mathematical Apparatus for Quantum-Theories: Based on the Theory of Boolean Lattices

Front Matter....Pages II-XI
General tribes (Boolean lattices)....Pages 1-44
Special theorems on Boolean Lattices....Pages 44-130
Important auxiliaries....Pages 130-145
General theory of traces....Pages 145-173
The tribe of figures on the plane....Pages 173-206
The trace-theorem....Pages 206-252
The lattice of subspaces of the Hilbert-Hermite space....Pages 252-285
Tribes of spaces....Pages 285-335
Double scale of spaces....Pages 335-386
Linear operators permutable with a projector....Pages 386-391
Some double Stieltjes’ and Radons integrals....Pages 391-402
Maximal normal operator and its canonical representation....Pages 402-428
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 ....Pages 428-450
Operational calculus on general maximal normal operators....Pages 450-462
Theorems on normal operators and on related canonical mapping....Pages 462-502
Some classical theorems on normal and selfadjoint operators....Pages 502-520
Multiplicity of spectrum of maximal normal operators....Pages 521-560
On items of operational calculus with application to the resolvent and spectrum of normal operators....Pages 560-586
Tribe of repartition of functions....Pages 586-622
Permutable normal operators....Pages 622-644
Approximation of somata by complexes....Pages 644-674
Vector fields on the tribe and their summation....Pages 675-689
Quasi-vectors and their summation....Pages 689-708
Summation of quasi-vectors in the separable and complete Hilbert-Hermite space....Pages 708-717
General orthogonal systems of coordinates in the separable and complete Hilbert-Hermite-space....Pages 718-724
Dirac’s Delta-function....Pages 724-760
Auxiliaries for a deeper study of summation of scalar fields....Pages 760-804
Upper and lower (DARS)-summation of fields of real numbers in a Boolean tribe in the absence of atoms....Pages 805-884
Upper and lower summation in the general case. Complete admissibility. Square summability of fields of numbers....Pages 884-941
Back Matter....Pages 942-952