On symbol analysis of periodic pseudodifferential operators

Zeitschrift für Analysis und ihre Anwendungen

Volumn 17, Issue 1, 1998, Pages 9-22

  Turunen, V ^a   Vainikko, G ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Asymptotic expansions; Periodic integral operators; Periodic pseudodifferential operators; Symbol analysis

Indexed keywords

EID: 26444553690     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/805     Document Type: Article

References (17)

1. Abramowitz, M. and I. A. Stegun: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 4th printing. New York: United States Department of Commerce 1965.
2. Agranovich, M. S.: Spectral properties of elliptic pseudodifferential operators on a closed curve. Fund. Anal. Appl. 13 (1979), 279 - 281.
3. Agranovich, M. S.: On elliptic pseudodifferential operators on a closed curve. Trans. Moscow Math. Soc. 47 (1985), 23 - 74.
4. Amosov, B. A.: On the approximate solution of elliptic pseudodifferential equations on a smooth closed curve (in Russian). Z. Anal. Anw. 9 (1990), 545 - 563.
5. Berthold, D. and B. Silbermann: Corrected collocation methods for periodic pseudodifferential equations. Numer. Math. 70 (1995), 397 - 425.
6. Elschner, J.: Singular Ordinary Differential Operators and Pseudodifferential Equations. Berlin: Akademie-Verlag 1985.
7. Kelle, O. and G. Vainikko: A fully discrete Galerkin method of integral and pseudodifferential equations on closed curves. Z. Anal. Anw. 14 (1995), 593 - 622.
8. McLean, W.: Local and global description of periodic pseudodifferential operators. Math. Nachr. 150 (1991), 151 - 161.
9. McLean, W., Prössdorf, S. and W. L. Wendland: A fully-discrete trigonometric collocation method. J. Int. Equ. Appl. 5 (1993), 103 - 129.
10. Saranen, J. and G. Vainikko: Trigonometric collocation methods with product integration for boundary integral equations on closed curves. SIAM J. Numer. Anal. 33 (1996), 1577 - 1596.
11. Saranen, J. and W. L. Wendland: The Fourier series representation of pseudo-differential operators on closed curves. Complex Variables 8 (1987), 55 - 64.
12. Steffensen, J. F.: Interpolation. 2nd ed. New York: Chelsea Publ. Comp. 1950.
13. Taylor, M.: Pseudodifferential Operators. Princeton: Univ. Press 1981.
14. Taylor, M.: Pseudodifferential Operators and Nonlinear PDE. Boston - Basel - Berlin: Birkhauser 1991.
15. Treves, F.: Introduction to Pseudodifferential and Fourier Integral Operators. New York: Plenum Press 1980.
16. Turunen, V.: Symbol Analysis of Periodic Pseudodifferential Operators. Master's Thesis. Helsinki: Univ. Techn. 1997.
17. Vainikko, G.: Periodic integral and pseudodifferential equations. Research report C13. Helsinki: Inst. Math. Univ. Techn. 1996.