54
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

On certain high-order partial differential expressions with δ-potential

Pages 255-261 | Received 01 Mar 2010, Published online: 17 May 2011

References

  • Akhiezer , N. I. and Glazman , I. M. 1981 . Theory of Linear Operators in Hilbert Space , Vol. 2 , Boston : Pitman .
  • Albeverio , S. and Koshmanenko , V. 1996 . “ Some remarks on the Gesztesy-Simon version of rank-one perturbations ” . Universität Bielefeld . preprint nr. 727/5/96
  • Albeverio , S. , Gesztesy , F. , Hoegh-Krohn , R. and Holden , H. 1988 . Solvable Models in Quantum Mechanics , New York : Springer-Verlag .
  • Antonevich , A. B. 1999 . The Schrödinger operator with δ-potential: Finite-dimensional perturbations approach . Nonlinear Phenom. Complex Syst , 2 : 61 – 71 .
  • Antonevich , A. and Radyno , Ya. 1991 . On general method of constructing of algebras of generalized functions . Dokl. AN USSR , 43 : 680 – 684 .
  • Antonevich , A. and Romanchuk , T. 2009 . On equations with δ-shaped coefficients: The finite-dimension perturbation approach . Integral Transforms Spec. Funct. , 3–4 : 239 – 246 .
  • Berezin , F. and Fadeev , L. 1961 . A remark on the Schrödinger equation with a singular potential . Soviet Math. Dokl. , 2 : 372 – 375 .
  • Christov , C. and Damianov , B. Asymptotic functions – a new class of generalized functions . Bulgar. J. Phys: part I-6 (1978), 543–556; part II-1 (1979), pp. 3–23; part III-3 (1979), pp. 245–256; part IV-4 (1979), 377–397
  • Colombeau , J. F. 1984 . New Generalized Functions and Multiplication of Distributions , Amsterdam : North-Holland . North-Holland Math. Stud. 84
  • Egorov , Yu. V. 1990 . A contribution to the theory of generalized functions . Uspekhi Mat. Nauk. , 45 : 3 – 40 .
  • Friedman , C. 1972 . Perturbations of the Schrödinger equation by potentials with small support . J. Funct. Anal. , 10 : 346 – 360 .
  • Gesztesy , F. and Simon , B. 1995 . Rank-one perturbations at infinite coupling . J. Funct. Anal. , 128 : 245 – 252 .
  • Oberguggenberger , M. 1992 . Multiplication of Distributions and Applications to Partial Differential Equations , Harlow : Longman . Pitman Research Notes Math., V. 259

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.