Special solution of the Sturm-Liouville equation with a complex potential

Return to list of articles
Doklady Bashkirskogo Universiteta. 2017. Volume 2. No. 3. pp. 366-370.

Authors

Yanturin I. A.
Bashkir State University
32 Zaki Validi Street, 450074 Ufa, Republic of Bashkortostan, Russia
Ishkin Kh. K.*
Bashkir State University
32 Zaki Validi Street, 450074 Ufa, Republic of Bashkortostan, Russia

Abstract

For a singular Sturm-Liouville equation with a complex smooth increasing potential we construct a special solution φ (x ,λ ) with following properties: a) for each λ∈C φ(∙,λ)∈ L 2 (0,+∞) , b) for each x≥0 φ x,∙ - an entire function of order 1/2+1/α .

Keywords

  • differential operators
  • Weyl solution
  • Weyl function
  • discretness of spectrum
Return to list of articles