Skip to main content
SpringerLink
Log in

On spectral theory for the linear selfadjoint equation Fy = λGy

  • Conference paper
  • First Online:
Ordinary and Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 846))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Bennewitz: Symmetric relations on a Hilbert-space Lecture Notes in Math. 280, Springer (1972), 212–218

    Google Scholar 

  2. C. Bennewitz: Spectral theory for pairs of differential operators. Ark.f.Math. 15 (1977), 33–61

    Article  MathSciNet  MATH  Google Scholar 

  3. F. Brauer: Singular selfadjoint boundary value problems for the differential equation Lx = λMx. Trans.Amer.Math.Soc. (1958), 331–345

    Google Scholar 

  4. F. Brauer: Spectral theory for linear systems of differential equations. Pac.Journ.Math. 10 (1960), 17–34

    Article  MathSciNet  MATH  Google Scholar 

  5. E.A. Coddington: Selfadjoint subspace extensions of non densely defined operators. Advances in Math. 14 (1974), 309–332

    Article  MathSciNet  MATH  Google Scholar 

  6. E.A. Coddington: Selfadjoint problems for non densely defined ordinary differential operators and their eigenfunction expansion. Advances in Math. 15 (1975), 1–40

    Article  MathSciNet  MATH  Google Scholar 

  7. E.A. Coddington: Eigenfunction expansions for selfadjoint subspaces generated by symmetric ordinary differential operators. Internat.conf.on diff.eq. Acad.Press Inc. (1975), 185–192

    Google Scholar 

  8. E.A. Coddington + A. Dijksma: Selfadjoint subspaces and eigenfunction expansions for ordinary differential subspaces. Journ.Diff.Equations 20 (1976), 473–526

    Article  MathSciNet  MATH  Google Scholar 

  9. E.A. Coddington + A. Dijksma: Adjoint subspaces in Banach spaces with applications to ordinary differential subspaces. Ann.Mat.pura.appl. 118 (1978), 1–118

    Article  MathSciNet  MATH  Google Scholar 

  10. E.A. Coddington + H.S.V. de Snoo: Positive selfadjoint extensions of positive symmetric subspaces. M.Z. 159 (1978), 203–214

    Article  MathSciNet  MATH  Google Scholar 

  11. E.A. Coddington + H.S.V. de Snoo: Differential subspaces associated with pairs of ordinary differential expressions. Journ.Diff.Equations 35 (1980), 129–182

    Article  MathSciNet  MATH  Google Scholar 

  12. A. Dijksma: Integral ordinary differential-boundary subspaces and spectral theory. Proc. of the Scheveningen conf. on diff.equat. (1975); North-Holland Publ. comp., 199–211

    Google Scholar 

  13. A. Dijksma + H.S.V. de Snoo: Symmetric subspaces related to certain eigenvalue problems. Comp.Math. 26 (1973), 233–247

    MathSciNet  MATH  Google Scholar 

  14. A. Dijksma + H.S.V. de Snoo: Selfadjoint extensions of symmetric subspaces. Pac. Journ.Math. 54 (1974), 71–100

    Article  MATH  Google Scholar 

  15. A. Dijksma + H.S.V. de Snoo: Eigenfunction expansions for non densely defined differential operators. Journ.Diff.Equations 17 (1975), 198–219

    Article  MATH  Google Scholar 

  16. H. Frentzen: On the left-definiteness of S-hermitian systems of differential equations. Questiones Math. 3 (1979), 281–312

    Article  MathSciNet  MATH  Google Scholar 

  17. I.M. Glazman: On the theory of singular differential operators. Amer.Math.Soc.Translations 96 (1953), 43 pp.

    Google Scholar 

  18. K. Kodaira: On ordinary differential equations of any even order and the corresponding eigenfunction expansion. Amer.Journ.Math. 72 (1950), 502–544

    Article  MathSciNet  MATH  Google Scholar 

  19. A.M. Krall: Differential-boundary operators. Trans.Amer.Math.Soc. 154 (1971), 429–458

    Article  MathSciNet  MATH  Google Scholar 

  20. A.M. Krall: The development of general differential and general differential-boundary systems. Rocky mountain. J. of Math. 5 (1975), 493–542

    Article  MathSciNet  MATH  Google Scholar 

  21. A.M. Krall: n-th order Stieltjes differential boundary operators and Stieltjes boundary systems. Journ.Diff.Equations 24 (1977), 253–267

    Article  MathSciNet  MATH  Google Scholar 

  22. H.D. Niessen: Singuläre S-herm. Rand-Eigenwertprobleme manuscripta math. 3 (1970), 35–68

    Article  MathSciNet  MATH  Google Scholar 

  23. H.D. Niessen: Spektraltheorie linksdefiniter Differenzengleichungssysteme. Journ.f.d. reine u.angew.Math. 278/279 (1975), 225–265

    MathSciNet  MATH  Google Scholar 

  24. H.D. Niessen + R. Mennicken: (S,\(\tilde S\))-adjungierte Randwertoperatoren. Math.Nachr. 44 (1970), 259–284

    Article  MathSciNet  MATH  Google Scholar 

  25. Å. Pleijel: Spectral theory for pairs of formally selfadjoint ordinary differential operators. J.Indian Math.Soc. 34 (1970), 259–268

    MathSciNet  MATH  Google Scholar 

  26. Å. Pleijel: A survey of spectral theory for pairs of ordinary differential operators. Lecture Notes in Math. 448, Springer (1975), 256–270

    Article  MathSciNet  MATH  Google Scholar 

  27. F.W. Schäfke + A. Schneider: S-hermitesche Rand-Eigenwertprobleme I. Math.Ann. 162 (1965), 9–26

    Article  MathSciNet  MATH  Google Scholar 

  28. F.W. Schäfke + A. Schneider: S-hermitesche Rand-Eigenwertprobleme II. Math.Ann. 165 (1966), 236–260

    Article  MathSciNet  MATH  Google Scholar 

  29. F.W. Schäfke + A. Schneider: S-hermitesche Rand-Eigenwertprobleme III. Math.Ann. 177 (1968), 67–94

    Article  MathSciNet  MATH  Google Scholar 

  30. A. Schneider: Zur Einordnung selbstadjungierter Rand-Eigenwertprobleme bei gewöhnlichen Differentialgleichungen in die Theorie S-herm. Rand-Eigenwertprobleme. Math.Ann. 178 (1968), 277–294

    Article  MathSciNet  MATH  Google Scholar 

  31. A. Schneider: Die Green'sche Matrix S-herm. Rand-Eigenwertprobleme im Normalfall. Math.Ann. 180 (1969), 307–312

    Article  MathSciNet  MATH  Google Scholar 

  32. A. Schneider: Untersuchungen über singuläre reelle S-hermitesche Differentialgleichungssysteme im Normalfall. M.Z. 107 (1968), 271–296

    Article  MATH  Google Scholar 

  33. A. Schneider: Weitere Untersuchungen über singuläre reelle S-herm. Differentialgleichungssysteme im Normalfall. M.Z. 109 (1969), 153–168

    Article  MATH  Google Scholar 

  34. A. Schneider: Zum Entwicklungssatz bei reellen singulären Differentialgleichungssystemen. Arch.d.Math. 21 (1970), 192–197

    Article  MATH  Google Scholar 

  35. A. Schneider: S-hermitian boundary-value problems for difference systems. Journ. f.d.reine u.angew.Math. 280 (1976), 70–76

    MathSciNet  MATH  Google Scholar 

  36. A. Schneider: On spectral theory for singular S-hermitian difference-systems. Journ.f.d.reine u.angew.Math. 280 (1976), 77–90

    MathSciNet  MATH  Google Scholar 

  37. A. Schneider + H.D. Niessen: Linksdefinite singuläre kanonische Eigenwertprobleme I. Journ.f.d.reine u.angew.Math. 281 (1976), 13–52

    MathSciNet  MATH  Google Scholar 

  38. A. Schneider + H.D. Niessen: Linksdefinite singuläre kanonische Eigenwertprobleme II. Journ.f.d.reine u.angew.Math. 289 (1977), 62–84

    MathSciNet  MATH  Google Scholar 

  39. H. Weyl: Über gewöhnliche Differentialgleichungen mit singulären Stellen und ihre Eigenfunktionen. Göttinger Nachr. (1910), 442–467

    Google Scholar 

  40. H. Weyl: Über gewöhnliche Differentialgleichungen mit Singularität und die zugehörige Entwicklung willkürlicher Funktionen. Math.Ann. 68 (1910), 220–269

    Article  MathSciNet  MATH  Google Scholar 

  41. H. Wielandt: Über die Eigenwertaufgaben mit reellen diskreten Eigenwerten. Math.Nachr. 4 (1950/51), 308–314

    Article  MathSciNet  MATH  Google Scholar 

  42. H.J. Zimmerberg: Symmetric Integro-Differential-Boundary Problems. Trans.Amer.Math.Soc. 188 (1974), 407–417

    Article  MathSciNet  MATH  Google Scholar 

  43. H.J. Zimmerberg: Linear integro-differential-boundary-parameter problems. Ann.Mat.Pura appl. 105 (1975), 241–256

    Article  MathSciNet  MATH  Google Scholar 

  44. A. Schneider: Selfadjoint boundary-value problems with differential boundary-value equations. to appear

    Google Scholar 

  45. H. Röh: Self-adjoint subspace extension satisfying λ-linear boundary conditions. to appear in: Proc.Royal Math.Soc.,Edinburgh

    Google Scholar 

Download references

Authors
  1. Albert Schneider
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

W. N. Everitt B. D. Sleeman

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Schneider, A. (1981). On spectral theory for the linear selfadjoint equation Fy = λGy. In: Everitt, W.N., Sleeman, B.D. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089848

Download citation

  • DOI: https://doi.org/10.1007/BFb0089848

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10569-5

  • Online ISBN: 978-3-540-38538-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation