J. Duistermaat

Publications134
h-index28
Citations5,606
Highly Influential Citations558
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The spectrum of positive elliptic operators and periodic bicharacteristics
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…
Fourier integral operators. II
On global action‐angle coordinates
On the variation in the cohomology of the symplectic form of the reduced phase space
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
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
On the Morse index in variational calculus
The heat kernel Lefschetz fixed point formula for the spin-c dirac operator
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"
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
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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