Some embedding properties of Hilbert subspaces in topological vector spaces

Eberhard Gerlach

Annales de l'institut Fourier (1971)

  • Volume: 21, Issue: 3, page 1-12
  • ISSN: 0373-0956

Abstract

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A general theorem on Hilbert subspaces of dually nuclear spaces is proved, from which all previous results of K. Maurin and the writer on regularity of generalized eigenfunctions follow as simple corollaries. In addition some supplements to L. Schwartz’s work on Hilbert subspaces in spaces of smooth functions are given.

How to cite

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Gerlach, Eberhard. "Some embedding properties of Hilbert subspaces in topological vector spaces." Annales de l'institut Fourier 21.3 (1971): 1-12. <http://eudml.org/doc/74047>.

@article{Gerlach1971,
abstract = {A general theorem on Hilbert subspaces of dually nuclear spaces is proved, from which all previous results of K. Maurin and the writer on regularity of generalized eigenfunctions follow as simple corollaries. In addition some supplements to L. Schwartz’s work on Hilbert subspaces in spaces of smooth functions are given.},
author = {Gerlach, Eberhard},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {1-12},
publisher = {Association des Annales de l'Institut Fourier},
title = {Some embedding properties of Hilbert subspaces in topological vector spaces},
url = {http://eudml.org/doc/74047},
volume = {21},
year = {1971},
}

TY - JOUR
AU - Gerlach, Eberhard
TI - Some embedding properties of Hilbert subspaces in topological vector spaces
JO - Annales de l'institut Fourier
PY - 1971
PB - Association des Annales de l'Institut Fourier
VL - 21
IS - 3
SP - 1
EP - 12
AB - A general theorem on Hilbert subspaces of dually nuclear spaces is proved, from which all previous results of K. Maurin and the writer on regularity of generalized eigenfunctions follow as simple corollaries. In addition some supplements to L. Schwartz’s work on Hilbert subspaces in spaces of smooth functions are given.
LA - eng
UR - http://eudml.org/doc/74047
ER -

References

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  1. [1] N. ARONSZAJN, Private communication. 
  2. [2] Heinz BAUER, Harmonische Räume und ihre Potential theorie, (Lecture Notes Math., N° 22). Springer-Verlag, Berlin, 1966. Zbl0142.38402
  3. [3] E. GERLACH, On spectral representation for selfadjoint operators, Expansion in generalized eigenelements, Ann. Inst. Fourier (Grenoble) 15 (1965), fasc. 2, 537-574. Zbl0135.16702MR32 #8172
  4. [4] E. GERLACH, On the analyticity of generalized eigenfunctions (case of real variables), Ibid. 18 (1968), fasc. 2, 11-16. Zbl0175.43501MR52 #11641
  5. [5] E. GERLACH, Mean value properties of generalised eigenfunctions, Proceedings Edinburgh Math. Soc. (2) 17 (1970), 155-158. Zbl0204.13504
  6. [6] A. MARTINEAU, Sur la topologie des espaces de fonctions holomorphes, Math. Ann. 163 (1966), 62-88. Zbl0138.38101MR32 #8109
  7. [7] K. MAURIN, Analyticity of generalized eigenfunctions, Bull. Acad. Polon. Sci., Sér. sci. math. astr. phys. 14 (1966), 685-687. Zbl0167.13705MR34 #8232
  8. [8] K. MAURIN, General eigenfunction expansions on harmonic spaces, Existence of reproducing kernels, Ibid. 15 (1967), 503-507. Zbl0167.13801MR38 #1542
  9. [9] K. MAURIN, Holomorphicity of generalized eigenfunctions on complex spaces, Ibid. 15 (1967), 607-610. Zbl0167.13802MR38 #562
  10. [10] A. PIETSCH, Nukleare lokalkonvexe Räume, Akademie-Verlag, Berlin, 1965. Zbl0152.32302
  11. [11] L. SCHWARTZ, Sous-espaces hilbertiens d'espaces vectoriels topologiques et noyaux associés, (Noyaux reproduisants), J. Analyse Math. 13 (1964), 115-256. Zbl0124.06504MR31 #3835

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