Asymptotics of spectrum and eigenfunctions for nonselfadjoint operators generated by radial nonhomogeneous damped wave equations

Asymptotic Analysis

Volumn 16, Issue 3-4, 1998, Pages 245-272

  Shubov, Marianna A ^a  

^a TEXAS TECH UNIVERSITY   (United States)

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[No Author keywords available]

Indexed keywords

EID: 0000011573     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. M. Abramovitz and I. Stegun, eds, Handbook of Mathematical Functions, Dover, New York, 1972.
2. S.A. Avdonin and I. Joo, Riesz bases of exponentials and sine-type functions, Acta Math. Hung. 51(1/2) (1988), 3-14.
3. N. Dunford and J.T. Schwartz, Linear Operators, III. Spectral Operators, New York, 1971.
4. 2 in linear combinations of exponentials, Notes Kharkov Univ., Math 30(4) (1964), 18-29.
5. A.S.B. Holland, Introduction to the Theory of Entire Functions, Academic Press, New York, 1973.
6. 2(-T,T), J. Operator Theory 14 (1985), 67-85.
7. S.V. Hruščev, N.K. Nikol'skii and B.S. Pavlov, Unconditional bases of exponentials and of reproducing kernals, in: Complex Analysis and Spectral Theory, Lecture Notes in Math., Vol. 864, Springer, 1981, pp. 215-335.
8. B.Ya. Levin, Distribution of Zeroes on Entire Functions, Transl. Math. Monographs, Vol. 5, AMS, Providence, RI, 1964.
9. W. Magnus, F. Oberhettinger and R.P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Springer, New York, 1966.
10. A.S. Marcus, Introduction to the Spectral Theory of Polynomial Pencils, Transl. Math. Monographs, Vol. 71, AMS, Providence, RI, 1988.
11. R.G. Newton, Scattering Theory of Waves and Particles, 2nd edn, Springer, New York, 1982.
12. N.K. Nikol'skii and B.S. Pavlov, Eigenvector bases of completely nonunitary contractions and the characteristic function, Math. USSR Izv. 4 (1970).
13. N.K. Nikol'skii, Treatise on the Shift Operator, Springer, Berlin, 1986.
14. B.S. Pavlov, Spectral analysis of differential operator with a "blurred" boundary condition, Problemy Matematicheskoi Fiziki 6 (1973), 101-119 (in Russian).
15. A.C. Pipkin, A Course on Integral Equations, Texts in Applied Math., Vol. 9, 1991.
16. J. Prüss, Evolutionary Integral Equations and Applications, Monographs in Math., Vol. 87, 1993.
17. M.A. Shubov, Basis property of eigenfunctions of nonselfadjoint operator pencils generated by the equation of non-homogeneous damped string, Integral Equations Operator Theory 25 (1996), 289-328.
18. M.A. Shubov, Asymptotics of resonances and geometry of resonance states in the problem of scattering of acoustical waves by a spherically symmetric inhomogeneity of the density, Differential Integral Equations 8(5) (1995), 1073-1115.
19. M.A. Shubov, Asymptotics of resonances and eigenvalues for nonhomogeneous damped string, Asympt. Anal. 13 (1996), 31-78.
20. M.A. Shubov, C.F. Martin, J.P. Dauer and B.P. Belinskiy, Unique controllability of the damped wave equation, SIAM J. Contr. Opt. 35(5) (1997), 1773-1789.
21. M.A. Shubov, Exact boundary and distributed controllability of nonhomogeneous damped string, to appear in J. Math. Pures Appl.
22. R.M. Young, An Introduction to Nonharmonic Fourier Series, Academic Press, New York, 1980.
23. A.M. Sedletskii, Biorthogonal decomposition of functions in exponential series on real intervals, Uspekhi Mat. Nauk 37(5) (1982), 57-95.
24. S.A. Avdonin and S.A. Ivanov, Families of Exponentials, Cambridge University Press, 1995.