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The spectrum of positive elliptic operators and periodic bicharacteristics
- J. Duistermaat, V. Guillemin
- Mathematics
- 1 February 1975
Let X be a compact boundaryless C ∞ manifold and let P be a positive elliptic self-adjoint pseudodifferential operator of order m>0 on X. For technical reasons we will assume that P operates on…
On the variation in the cohomology of the symplectic form of the reduced phase space
- J. Duistermaat, G. Heckman
- Mathematics
- 1 June 1982
is called the momentum mapping of the Hamiltonian T-action. Given (1.1), the condition (1.2) just means that T acts along the fibers of J. For the basic definitions and properties of non-commutative…
Differential equations in the spectral parameter
- J. Duistermaat, F. Grünbaum
- Mathematics
- 1 June 1986
We determine all the potentialsV(x) for the Schrödinger equation (−∂x2+V(x))∅=k2∅ such that some family of eigenfunctions ∅ satisfies a differential equation in the spectral parameterk of the…
Oscillatory integrals, lagrange immersions and unfolding of singularities
- J. Duistermaat
- Mathematics
- 1 March 1974
The heat kernel Lefschetz fixed point formula for the spin-c dirac operator
- J. Duistermaat
- Mathematics
- 1 February 1996
1 Introduction.- 2 The Dolbeault-Dirac Operator.- 3 Clifford Modules.- 4 The Spin Group and the Spin-c Group.- 5 The Spin-c Dirac Operator.- 6 Its Square.- 7 The Heat Kernel Method.- 8 The Heat…
Selfsimilarity of "Riemann's nondifferentiable function"
- J. Duistermaat
- Mathematics
- 24 April 1994
This is an expository article about the series f(x) = 1 X n=1 1 n 2 sin(n 2 x); which according to Weierstrass was presented by Riemann as an example of a continuous function without a derivative. An…
Spectra of compact locally symmetric manifolds of negative curvature
- J. Duistermaat, J. Kolk, V. Varadarajan
- Mathematics
- 1 February 1979
Let S be a Riemannian symmetric space of noncompact type, and let G be the group of motions of S. Then the algebra L-~ of G-invariant differential operators on S is commutative, and its spectrum A(S)…
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