The FBI transform on compact ${\mathcal {C}^\infty }$ manifolds

The Fbi Transform on Compact C∞ Manifolds

We present a geometric theory of the Fourier-Bros-Iagolnitzer transform on a compact C∞ manifold M . The FBI transform is a generalization of the classical notion of the wave-packet transform. We discuss the mapping properties of the FBI transform and its relationship to the calculus of pseudodifferential operators on M . We also describe the microlocal properties of its range in terms of the “...

The Fbi Transform on Compact C1 Manifolds

Cubature formulas and discrete fourier transform on compact manifolds

Analysis on two dimensional surfaces and in particular on the sphere S found many applications in computerized tomography, statistics, signal analysis, seismology, weather prediction, and computer vision. During last years many problems of classical harmonic analysis were developed for functions on manifolds and especially for functions on spheres: splines, interpolation, approximation, differe...

Surgery on Compact Manifolds

Lipschitz Spaces on Compact Manifolds

Let f be a bounded function on the real line IF!. One may characterize the structural properties off by the modulus of smoothness w(t,f) = sup{lf (4 -f( y)l; x, y E 08, I x y I < t>, and, if w(t) is a continuous nondecreasing function of t > 0 such that w(O) = 0, by the Lipschitz class Lip(w) which is the set of all continuous functions such that su~~<~<i w(t, f)/o(t) < 00. It is possible to ex...