On spectral representation for selfadjoint operators. Expansion in generalized eigenelements

Eberhard Gerlach

Annales de l'institut Fourier (1965)

  • Volume: 15, Issue: 2, page 537-574
  • ISSN: 0373-0956

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Gerlach, Eberhard. "On spectral representation for selfadjoint operators. Expansion in generalized eigenelements." Annales de l'institut Fourier 15.2 (1965): 537-574. <http://eudml.org/doc/73884>.

@article{Gerlach1965,
author = {Gerlach, Eberhard},
journal = {Annales de l'institut Fourier},
keywords = {functional analysis},
language = {eng},
number = {2},
pages = {537-574},
publisher = {Association des Annales de l'Institut Fourier},
title = {On spectral representation for selfadjoint operators. Expansion in generalized eigenelements},
url = {http://eudml.org/doc/73884},
volume = {15},
year = {1965},
}

TY - JOUR
AU - Gerlach, Eberhard
TI - On spectral representation for selfadjoint operators. Expansion in generalized eigenelements
JO - Annales de l'institut Fourier
PY - 1965
PB - Association des Annales de l'Institut Fourier
VL - 15
IS - 2
SP - 537
EP - 574
LA - eng
KW - functional analysis
UR - http://eudml.org/doc/73884
ER -

References

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  1. [1] N. ARONSZAJN, Theory of reproducing kernels, Trans. Am. Math. Soc., 68, (1950), 337-404. Zbl0037.20701MR14,479c
  2. [2] Yu. M. BEREZANSKIĬ, On the expansion in eigenfunctions of selfadjoint operators, Ukr. Mat. Žurnal, 111, (1959), 16-24. (In Russian). Zbl0092.12401
  3. [3] N. DUNFORD and J. SCHWARTZ, Linear Operators. Part II: Spectral Theory. Selfadjoint Operators in Hilbert Space, Interscience (J. Wiley), New-York, 1963. Zbl0128.34803
  4. [4] C. FOIAS, Décompositions intégrales des familles spectrales et semi-spectrales en opérateurs qui sortent de l'espace hilbertien, Acta Scient. Math. (Szeged), 20, (1959), 117-155. Zbl0092.12402MR22 #5895
  5. [5] C. FOIAS, Décompositions en opérateurs et vecteurs propres. I. Études de ces décompositions et leurs rapports avec les prolongements des opérateurs, Revue de math. pures et appl., 7, (1962), 241-282.— II. Éléments de théorie spectrale dans les espaces nucléaires, Revue math. pur. appl., 7, (1962), 571-602. Zbl0204.15601MR35 #770
  6. [6] H. HAHN, Uber die Integrale des Herrn Hellinger und die Orthogonalinvarianten der quadratischen Formen von unendlich vielen Veränderlichen, Monats h. für Math. und Physik, 23, (1912), 161-224. Zbl43.0421.03JFM43.0421.03
  7. [7] E. HELLINGER, Neue Begründung der Theorie quadratischer Formen von unendlich vielen Veränderlichen, J. reine angew. Math., 136, (1909), 210-271. Zbl40.0393.01JFM40.0393.01
  8. [8] G. I. KAC, Generalized elements of Hilbert space, Ukr. Mat. Ž., 121, (1960), 13-24. (In Russian). 
  9. [9] G. I. KAC, Spectral decompositions of selfadjoint operators relative to generalized elements of Hilbert space, Ukr. Mat. Ž., 134, (1960), 13-33. (In Russian). 
  10. [10] G. I. KAC, Generalized functions on a locally compact group and decompositions of unitary representations, Trudy Moskov. Mat. Obščestva, 10, (1961), 3-40. (In Russian). 
  11. [11] K. MAURIN, Spektraldarstellung der Kerne. Eine Verallgemeinerung der Sätze von Källén-Lehmann und Herglotz-Bochner u.a, Bull. Acad. Polon. Sci. Sér. sci. math. astr. phys., 7, (1959), 461-470. Zbl0106.08902MR22 #4959
  12. [12] K. MAURIN, Allgemeine Eigenfunktionsentwicklungen. Spektraldarstellung der Kerne. Eine Verallgemeinerung der Distributionen auf Lie'sche Gruppen, ibid., 7, (1959), 471-479. Zbl0106.08903MR22 #4960
  13. [13] K. MAURIN, Abbildungen vom Hilbert-Schmidtschen Typus und ihre Anwendungen, Math. Scand., 9, (1961), 359-371. Zbl0107.32702MR25 #4364
  14. [14] H. MESCHKOWSKI, Hilbertsche Räume mit Kernfunktion, Springer Verlag, Berlin, 1962 (Grundlehren der math. Wissenschaften..., Band 113). Zbl0103.08802MR25 #4326
  15. [15] J. Von NEUMANN, On rings of operators. Reduction theory, Ann. of Math., (2), 50, (1949), 401-485. Zbl0034.06102MR10,548a
  16. [16] M. H. STONE, Linear transformations in Hilbert space, Am. Math. Soc. Colloquium Publications, vol. XV, 1932. Zbl0005.40003JFM58.0420.02

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