JÓZEF DODZIUK

PUBLICATIONS

1. On measurable periodic functions, (in Polish), Wiadomosci Matematyczne, XI (1969), 13-14.

2. Combinatorial and continuous Hodge theories, Bull. Amer. Math. Soc., 80 (1974),1014-1016.

3. Finite difference approach to the Hodge theory of harmonic forms, Amer. J. Math., 98 (1976), 79-104.

4. A remark on Whitney's proof of de Rham's theorem, Proc. Amer. Math. Soc., 54 (1976), 360-362.

5. Riemannian structures and triangulations of manifolds (with V.  K. Patodi), J. Indian Math. Soc., 40 (1976), 1-52.

6. De Rham-Hodge theory for $L^2$-cohomology of infinite coverings, Topology, 16 (1977), 157-165.

7. $L^2$ harmonic forms on rotationally symmetric Riemannian manifolds, Proc. Amer. Math. Soc., 77 (1979), 395-400.

8. Vanishing theorems for $L^2$ harmonic forms, in Geometry and Analysis, Papers dedicated to the memory of V. K. Patodi, Indian Academy of Sciences and Tata Institute of Fundamental Research, Bombay 1980, 21-27.

9. Sobolev spaces of differential forms and the de Rham-Hodge isomorphism, J. Differential Geometry, 16 (1981), 63-73.

10. Eigenvalues of the Laplacian and the heat equation, Amer. Math. Monthly, 88 (1981), 686-695.

11. $L^2$ harmonic forms on complete manifolds, in Seminar on Differential Geometry, S.-T. Yau Ed., Princeton University Press, Princeton N. J. 1982, 291-302.

12. $L^2$ isolation theorem for Yang-Mills fields over complete manifolds (with Min-Oo), Compositio Math., 47 (1982), 291-302.

13. Eigenvalues of the Laplacian on forms, Proc. Amer. Math. Soc., 85 (1982), 437-443.

14. Maximum principle for parabolic inequalities and the heat flow on open manifolds, Indiana University Math. J., 32 (1983), 703-716.

15. Every covering of a compact Riemann surface of genus greater than one carries a nontrivial $L^2$ harmonic differential, Acta Mathematica, 152 (1984), 49-56.

16. Difference equations, isoperimetric inequality and transience of certain random walks, Trans. Amer. Math. Soc., 284 (1984), 787-794.

17. Laplacian on forms, appendix to Eigenvalues in Riemannian Geometry, by I. Chavel, Academic Press, 1984.

18. Laplacian on manifolds and analogous difference operator for graphs, Contemporary Mathematics, 49 (1986), 45-49.

19. Review of Invariance theory, the heat equation, and the Atiyah-Singer index theorem, by P. Gilkey, Bull. Amer. Math. Soc., 14 (1986), 322-325.

20. Lower bounds for $\lambda_1$ on a finite volume hyperbolic manifold (with B. Randol), J. Differential Geometry, 24 (1986), 133-139.

21. Combinatorial Laplacians and isoperimetric inequality (with W. S. Kendall), in From local times to global geometry, control and physics, K. D. Ellworthy Ed., Pitman Research Notes in Mathematics Series, 150 (1986), 68-74.

22. Estimating small eigenvalues of Riemann surfaces (with T.  Pignataro, B. Randol and D. Sullivan), Contemporary Mathematics 64 (1987), 93-121.

23. A lower bound for the first eigenvalue of a finite-volume negatively curved manifold, Bol. Soc. Bras. Mat., 18 (1987), 23-34.

24. Compact Riemann surfaces of large genus with large $\lambda_1$ (with M. Burger and P. Buser), in Geometry and Analysis on Manifolds, T. Sunada Ed., Lecture Notes in Mathematics 1339 (1988), 54-63.

25. Laplacian on Graphs - Spectral and Function Theory (with L.  Karp), Contemporary Mathematics, 73 (1988), 25-40.

26. Small eigenvalues of the Laplacian on negatively curved manifolds (with P. Buser and B. Colbois), in Differential Geometry, R. Greene and S. T. Yau, eds., Proceedings of Symposia in Pure Mathematics 54, American Mathematical Society, Providence, Rhode Island, 1993.

27. Tubes and eigenvalues for negatively curved manifolds (with P. Buser and B. Colbois), J. Geometric Analysis, 3 (1993), 1-26.

28. The spectrum of degenerating hyperbolic manifolds of three dimensions (with I. Chavel), J. Differential Geometry, 39 (1994), 123-137.

29. Riemannian Metrics with Large $\lambda_1$ (with B. Colbois), Proc. Amer. Math. Soc., 122 (1994), 905-906.

30. Nonexistence of universal upper bounds for the first positive eigenvalue of the Laplace-Beltrami operator, in Proceedings of the 1993 Joint Summer Research Conference on Spectral Geometry, Contemporary Mathematics, 173 (1994).

31. The spectrum of the Hodge Laplacian for a degenerating family of hyperbolic three manifolds (with J. McGowan), Trans. Amer. Math. Soc., 347 (1995), 1981-1995.

32. La trace du noyau de la chaleur des variétés hyperboliques de dimension 3, Séminaire de théorie spectrale et géométrie, (1995-1996), Grenoble.

33. A ${\cal C}^\infty$ Spline Construction (with P. Blass, T. J. Ford, J. Kolibal), Ulam Quarterly, 3 (1996), 11-19.

34. Continuity of Spectra of Hodge-de Rham Laplacian (with G. Baker), Math. Z., 224 (1997), 327-345.

35. On the geometry and spectral asymptotics of degenerating hyperbolic manifolds (with Jay Jorgenson), in ``Extremal Riemann Surfaces'', Contemporary Mathematics, 201 (1997), 191-206.

36. Approximating $L^2$ invariants of amenable covering spaces: A heat kernel approach (with Varghese Mathai), in ``Lipa's Legacy'', Contemporary Mathematics, 211 (1997), 151-167.

37. Spectral asymptotics on degenerating hyperbolic three manifolds (with J. Jorgenson), Memoirs of Amer. Math. Soc., 643 (1998).

38. Approximating $L^2$ invariants of amenable covering spaces: A combinatorial approach (with Varghese Mathai), J. Functional Analysis, 154 (1998), 359-378.

39. Integral Structures on $\mathbf H$-type Lie Algebras (with Gordon Crandall), J. Lie Theory, 12 (2002), 69-79.

40. Approximating $L^2$-Invariants and the Atiyah Conjecture (with P. Linnell, T. Schick, M. Varghese and S. Yates), Comm. Pure Appl. Math., 56, no. 7, (2003), 839-873.

41. Arithmetic properties of eigenvalues of generalized Harper operators on graphs (with M. Varghese and S. Yates), Comm. Math. Physics, 262 (2006), 269-297, http://xxx.lanl.gov/abs/math.SP/0311315 .

42. Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians (with M. Varghese), in ``Ubiquitous Heat Kernel'', Contemporary Mathematics, 398 (2006), 69-81, http://xxx.lanl.gov/abs/math.SP/0312450.

43. Elliptic operators on infinite graphs, in proceedings of the conference "Krzysztof Wojciechowski 50 years - Analysis and Geometry of Boundary Value Problems," Roskilde, Denmark, (2006), 353-368 http://xxx.lanl.gov/abs/math.SP/0509193.