Donald A. Lutz

Phone Number: 594-6806
Office: BA-209
E-mail: lutz@math.sdsu.edu

Department of Mathematical and Computer Sciences
San Diego State University
5500 Campanile Drive
San Diego, CA 92182-7720

 

Current Courses:
Education: B.S.    Syracuse University,  1961, Mathematics
M.S.   Syracuse University,  1963, Mathematics
Ph.D.  Syracuse University,  1965, Mathematics
Thesis:

"On the characterization of systems of differential equations having regular singular solutions"

Advisor:  Wolfgang B. Jurkat
Positions:  
  • Assistant Professor, University of Wisconsin-Milwaukee, 1965-1970

  • Visiting Lecturer, University of Maryland, 1967-1968

  • Visiting Assistant Professor, University of Wisconsin-Madison, 1969-1970

  • Associate Professor, University of Wisconsin-Milwaukee, 1970-1978

  • Visiting Associate Professor, University of Southern California, 1973

  • Humboldt Fellow, University of Ulm, 1975-76

  • Professor, University of Wisconsin-Milwaukee, 1978-1987

  • Visiting Professor, University of Southern California, 1985-86

  • Humboldt Fellow, University of Ulm, 1986

  • Professor, San Diego State University,  1986-present

  • Visiting Professor (invite), University  Louis Pasteur,  Strasbourg, France,Summer 1989, 1990, 1994, 1996

  • Visiting Professor, University of Essen, Germany, September 1992-March 1993.

  • Professeur Associe,  Universite Angers,  May, 1998, Sept 2000-March 2001.

  • Visiting Foreign Scholar, Kumamoto University, Dec 1999-March 2000

Military Service: 
  • US Army (active duty), 1966-1968, Captain.
  • US Army Reserve, 1968-1992, Retired with rank of Lieutenant Colonel.
Articles in refereed Journals:
  1. Some characterizations of systems of linear differential equations having regular singular solutions, Trans. Amer. Math. Soc. 126 (1967) 427-441.

  2. On systems of linear differential equations having regular singular solutions,  Jour. Diff. Eqns.  3  (1967) 311-322.

  3. Asymptotic behavior of solutions of linear systems of ordinary differential equations near an irregular singular point, Amer. Jour. Math. 91 (1969) 95-105.

  4. Perturbations of matrix differential equations in the neighborhood of a singular point, Funkcialaj Ekvacioj, 13 (1970) 97-107.

  5. On the order of solutions of analytic linear differential equations, Proc. London Math. Soc. 3rd Ser. 22 (1971) 465-482 (with W.B. Jurkat).

  6. On the reduction of rank of linear differential equations, Pac. Jour. Math. 42 (1972) 153-164.

  7. On the asymptotic integration of linear differential systems, Jour. Math. Anal. Appl.  (with W.A. Harris, Jr.).  48 (1974), 1-16.

  8. Birkhoff invariants and effective calculations for meromorphic linear differential equations I, Jour. Math. Anal. Appl. 53 (1976) 438-470 (with W.B. Jurkat and A. Peyerimhoff).

  9. Birkhoff invariants and effective calculations for meromorphic linear differential equations II, Houston Math. Jour. 2 (1976) 207-238 (with W.B. Jurkat and A. Peyerimhoff).

  10.  On the asymptotic integration of adiabatic oscillators, J. Math. Anal. Appl. 51 (1975) 76-93 (with W.A. Harris, Jr.).

  11. On a unified theory of asymptotic integration, J. Math. Anal. Appl.  57 (1977) 571-586 (with W.A. Harris, Jr.).

  12. A general theory of invariants for meromorphic differential equations (with W. Balser and W.B. Jurkat);

  13. Part I,  Formal Invariants, Funk. Ekvac. 22 (1979) 197-221,

  14. Part II,  Proper Invariants,  Funk Ekvac. 22 (1979) 257-283,

  15. Part III,Applications, Houston Jour. Math 6 (1980) 149-189.

  16. Birkhoff invariants and Stokes' multipliers for meromorphic differential equations (with W. Balser and W.B. Jurkat),  J. Math. Anal. Appl. 77 (1979) 48-94.

  17. Invariants for reducible systems of meromorphic differential equations (with W. Balser and W.B. Jurkat), Proc. Edin. Math. Soc. 23 (1980) 163-186.

  18. On the reduction of connection problems for differential equations with an irregular singular point to ones with only regular singularities (with W. Balser and W.B. Jurkat);  Part I,  SIAM Jour. on Math. Anal. 12 (1981) 691-721.

  19. Transfer of connection problems for meromorphic differential equations of rank  r ≥ 2 and representations of solutions, Jour. Math. Anal. Appl. 85 (1982) 488-542 (with W. Balser and W.B. Jurkat).

  20. Transfer of connection problems for first level formal solutions of meromorphic differential equations, and associated Laplace transforms  (with W. Balser and W.B. Jurkat), Jour. für die reine und angewandte Math., 344 (1983) 149-170.

  21. Characterization fo first level formal solutions by means of the growth of their coefficients (with W. Balser and W.B. Jurkat), Jour. of diff. Equations, 51 (1984) 48-77.

  22. On the identification and stability of formal invariants for singular differential equations (with R. Schafke), Linear Algebra and Applications, 72 (1985) 1-46.

  23. On the reduction of connection problems for differential equations with an irregular singular point to ones with only regular singularities, Part II, (with W. Balser and W.B. Jurkat), S.I.A.M. Jour. Math. Anal., 1988, no. 2, 398-443.

  24. Asymptotic representation of solutions of perturbed systems of linear difference equations, (with Z. Benzaid). Studies in Appl. Math, 77(1987) 195-221.

  25. Constrained controllability of perturbed discrete-time systems  (with Z. Benzaid), Int. Jour. Control, 48 (1988) 655-673.

  26. Convergent factorial series solutions of singular operator equations (with R. Gerard), Analysis, (1990), 10, 99-145.

  27. Maillet type theorems for algebraic difference equations (with R. Gerard), Kumamoto Math Jour.(Japan), vol. 3, (1990), 11-26.

  28. Convergent factorial series expansions for Bessel Functions, (with T.M. Dunster), S.I.A.M. Journal on Math. Anal., 22 (1991) 1156-1172.

  29. On the remainders of the asymptotic expansion of solutions of differential equations near irregular singular points (with R. Schaefke),  Complex Variables, Theory & Appl. 26(1994) no. 3,203-212.

  30. Convergent Liouville-Green Expansions for second order differential equations, with an application to Bessel functions (with T. M. Dunster and R. Schaefke),  Proc. Royal Soc. London, Series A, (1993) 440, pp. 37-54.

  31. Analytic reduction of a class of nonlinear difference equations (with R. Gérard and R. Schaefke),  Funkcialaj Ekvacioj, 38 (1995)381-410.

  32. On the reduction of a class of nonhomogenous linear difference equations (with R. Schaefke),  Journal of Difference Equations and Applications,2 (1996) 423-436.

  33. Calculating connection coefficients for meromorphic differential equations (with R. Schaefke),   Complex Variables,Theory & Appl. 34 (1997) 145-170.

  34. On Borel summability of divergent solutions of the complex heat equation, (with M. Miyake & R. Schaefke)  Nagoya Jour. Math. vol.154 (1999) 1-29.

  35. On the convergence of Borel Approximants, (with W. Balser & R. Schaefke) submitted.

  36. Asymptotic behavior of dynamic equations on time scales (with M. Bohner), to appear in the Journal of Difference Equations and Applications, special issue in memory of W. A. Harris, Jr.

     

Articles in Refereed Proceedings
  1. Linear perturbations of irregular singular systems, Proc. U.S.-Japan Seminar on Differential Equations, 1967, University of Minnesota, W. A. Benjamin.

  2. Effective solutions for meromorphic second order differential equations (with W. Jurkat and A. Peyerimhoff), Symposium on Ordinary Differential Equations, Lecture Notes in Math. #312, Springer-Verlag, 1973, pp. 100-107.

  3. On the summation of formal solutions at an irregular singular point by factorial series, Int. Conf. on Differential Equations at USC, H. Autosiewicz, Ed., Academic Press, 1975, pp. 489-509.

  4. Recent results in the asymptotic integration of linear differential systems, (with W. A. Harris, Jr.), Int. Conf. on Differential Equations at USC, H. Autosiewicz, Ed., Academic Press, 1975, pp. 345-349.

  5. Invariants and canonical forms for meromorphic second order differential equations (with W. Jurkat and A. Peyerimhoff), New Developments in Differential Equations, W. Eckhaus, Ed., North-Holland Publ. Co., 1976, pp. 181-187.

  6. Connection problems in the parameterless case:  progress and more problems, Proc. Symposium on Singular Perturbations and Asymptotic at the Math. Res. Ctr., UW-Madison, S. Parter and R. Meyer, Ed., Academic Press, 1980, pp. 357-378.

Colloquiua and other invited addresses:

 

 

January, 1995 Special session on Exponential Asymptotics at the Issac Newton Institute, Cambridge University, England, series of 5 lectures on Borel transforms and their applications to a school on Exponential Asymptotics and their Applications.

In the past 10 years, I have given colloquium and seminar talks at the University of California-San Diego, University of Southern California, Syracuse University, the University of Ulm, the University of Stuttgart-Hohenheim, the University of Stuttgart (TH), the University of Essen, the University of Groningen, the University of Paris VII, the TU of Berlin, and the Academy of Sciences, Kiev, University of Tokyo, University of Paris, Technical University of Berlin, University of Grenoble, University of Paris, University of La Rochelle,  Kumamoto University (2001), University of Missouri-Rolla (2001), University of Strasbourg (1998), University of Rome (2001), Nagoya University (2000).

 

Work in progress:

Asymptotic expansions for solutions of dynamic equations on time-scales, with M. Bohner.

Calculation of Stokes multipliers for systems of differential equations with one-level, with M. Loday and R. Schaefke.

 

The information on personal home pages represents that of the author and not necessarily that of San Diego State University. The author takes full responsibility for the information presented.

 

 

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