Naimark, M.A. (1940) Spectral functions of a symmetric operators. Izvestiya Akademii Nauk SSSR, seriya mate-maticheskaya [in Russian, partially in English], 4, 277-318; we stress that it is used here the Carleman type of the spectral function of (a maximal and not only maximal ) symmetrical operator, which was cited from the reference [Carleman, T. (1923) Sur les e’quations i’ntegrales a’ noyau re’el et syme’trque (Uppsala)] and was utilized as a tool of the proof, based on the approxi-mation of the (maximal and not only maximal) symmet-ric operator H by such succession of the bounded self-adjoint operators, the spectral functions the spectral functions of which do weakly converge to the spectral function E (l) of the operator H (This circumstance was kindly indicated to the author by Holevo, A.S.).

has been cited by the following article:

• TITLE: A retrospective view on the history of natural sciences in XX-XXI

  AUTHORS: Vladislav Sergeyevich Olkhovsky

  KEYWORDS: science history; science realism; paradigm; problem of interpretation and comprehension of quantum mechanics; the wave-function collapse; the Einstein-Podolsky-Rosen paradox; time as a quantum observable, canonically conjugated to energy; maximal hermitian time operator; time analysis of quantum processes; relationship be-tween physics and biology; problem of origin of biologic life; reductionism; cosmologic problem; Big Bang; anthropic principle

  JOURNAL NAME: Natural Science, Vol.2 No.3, April 12, 2010

  ABSTRACT: The presented paper is dedicated to a new ret-rospective view on the history of natural sci-ences in XX-XXI cc, partially including the sci-ence philosophy (mainly, the problems of the scientific realism, i.e. the correspondence of science to reality) and also a novel scheme for different classes of sciences with different ob-jects and paradigms. There are analyzed the chosen “great” and “grand” problems of phys-ics (including the comprehension of quantum mechanics, with a recently elaborated new chapter, connected with time as a quantum obs- ervable and time analysis of quantum processes) and also of natural sciences as a whole. The particular attention is paid to the interpretation questions and slightly to the aspects, inevitably connected with the world- views of the res- earchers (which do often constitute a part of the interpretation questions).