On a non-local problem for irregular equations

Journal Article · Sun Dec 31 04:00:00 EST 2000 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2000V191N11ABEH000521; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21202984

Kornienko, V V ^[1]

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1. A. Navoi Samarkand State University, Samarkand (Uzbekistan)

We study the distribution on the complex plane C of the spectrum {sigma}L=P{sigma}L union C{sigma}L union R{sigma}L of the operator L generated by the closure in H=L{sub 2}(T{sub 1},T{sub 2})xH of an irregular operation a(t)D{sub t}+A originally defined on the smooth functions u(t):[T{sub 1},T{sub 2}]{yields}H that satisfy the non-local conditions: {mu}{center_dot}u(T{sub 1})-u(T{sub 2})=0. Here a(t)={sigma}{sub k=1}{sup 2}a{sub k}|t|{sup {alpha}{sub k}}{chi}{sub k}(t); a{sub k} element of C, a{sub k}{ne}0; {alpha}{sub k} element of R; {chi}{sub k}(t) is the characteristic function of the interval with end-points 0,T{sub k}; -{infinity}<T{sub 1}<0<T{sub 2}<+{infinity}; D{sub t}{identical_to}d/dt; A is a model operator acting in a Hilbert space H; {mu} element of C-bar, {mu}{ne}0,{infinity}.

• OSTI ID: 21202984
• Journal Information: Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 11 Vol. 191; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

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GENERAL PHYSICS
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HILBERT SPACE
SMOOTH MANIFOLDS