Abstract
A general class of phase-space decompositions f(x)=∝a(x,p) dp of functions f defined in ℝn is presented. In the latter, a(x,p) depends on values of the Fourier transform F of f in a region around p whose width tends to zero as |x| increases and it decays exponentially, for each p, in all directions in x-space outside the microsupport at p of F, with a rate of exponential fall-off linked to analyticity properties of F in local tubes (in complex space) around p. A possible application in quantum-field theory is mentioned.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
BrosJ. and IagolnitzerD., Ann. Inst. H. Poincaré 18(2), 147 (1973).
IagolnitzerD. in R.Balian and D.Iagolnitzer (eds), Structural Analysis of Collisions Amplitudes, North-Holland, Amsterdam, 1976, p. 295.
HörmanderL., Acta Math. 127, 79 (1971).
SatoM., KawaiT., and KashiwaraM., in Hyperfunctions and Pseudo-differential Equations, Lecture Notes in Mathematics, Springer-Verlag, Heidelberg, 1972.
Bony, J. M., Equivalence des diverses notions de spectre singulier analytique, Seminaire Goulaonic-Schwartz, Ecole Polytechnique, Palaiseau, 1976–77, expose No. 3.
Rivasseau, V., Perturbative and Constructive Renormalization, Princeton University Press (to be published).