Geodesic
Localization properties of~highly singular generalized functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 2, pp. 179-194

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We study the localization properties of generalized functions defined on a broad class of spaces of entire analytic test functions. This class, which includes all Gelfand–Shilov spaces $S^{\beta}_{\alpha}(\mathbb R^k)$ with $\beta1$, provides a convenient language for describing quantum fields with a highly singular infrared behavior. We show that the carrier cone notion, which replaces the support notion, can be correctly defined for the considered analytic functionals. In particular, we prove that each functional has a uniquely determined minimal carrier cone.
Keywords: generalized function, analytic functional, infrared singularity, carrier cone, plurisubharmonic function, Hörmander's $L_2$ estimates. 
@article{TMF_2007_151_2_a0,
     author = {A. G. Smirnov},
     title = {Localization properties of~highly singular generalized functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--194},
     publisher = {mathdoc},
     volume = {151},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_151_2_a0/}
}
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A. G. Smirnov. Localization properties of~highly singular generalized functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 2, pp. 179-194. http://geodesic.mathdoc.fr/item/TMF_2007_151_2_a0/