Localization properties of highly singular generalized functions

Theoretical and Mathematical Physics

Volumn 151, Issue 2, 2007, Pages 591-603

  Smirnov, A G ^a  

^a LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

Author keywords

Analytic functional; Carrier cone; Generalized function; H rmander's L 2 estimates; Infrared singularity; Plurisubharmonic function

Indexed keywords

EID: 34249012143     PISSN: 00405779     EISSN: 15739333     Source Type: Journal    
DOI: 10.1007/s11232-007-0046-8     Document Type: Article

References (16)

1. L. Hörmander, The Analysis of Linear Partial Differential Operators: I. Distribution Theory and Fourier Analysis (Grundlehren Math. Wiss., Vol. 256), Springer, Berlin (1983).
2. A. Z. Capri and R. Ferrari, J. Math. Phys., 25, 141 (1984).
3. R. F. Streater and A. S. Wightman, PCT, Spin and Statistics and All That, Benjamin, New York (1964).
4. E. Brüning and S. Nagamachi, J. Math. Phys., 30, 2340 (1989).
5. U. Moschella and F. Strocchi, Lett. Math. Phys., 24, 103 (1992).
6. M. A. Soloviev, Lett. Math. Phys., 33, 49 (1995).
7. M. A. Soloviev, Comm. Math. Phys., 184, 579 (1997).
8. I. M. Gel'fand and G. E. Shilov, Generalized Functions [in Russian], Vol. 2, Spaces of Fundamental and Generalized Functions, Fizmatgiz, Moscow (1958); English transl., Acad. Press, New York (1968).
9. A. G. Smirnov and M. A. Solov'ev, Theor. Math. Phys., 125, 1349 (2000).
10. I. M. Gel'fand and G. E. Shilov, Generalized Functions [in Russian], Vol. 3, Some Questions in the Theory of Differential Equations, Fizmatgiz, Moscow (1958);
11. English transl.: Vol. 3, Theory of Differential Equations, Acad. Press, New York (1967).
12. A. G. Smirnov, "On topological tensor products of functional Fréchet and DF spaces," arXiv:math/0512611v1 [math.FA] (2005).
13. H. Komatsu, J. Math. Soc. Japan, 19, 366 (1967).
14. H. H. Schaefer, Topological Vector Spaces, MacMillan, New York (1966).
15. V. S. Vladimirov, Methods of the Theory of Functions of Many Complex Variables [in Russian], Nauka, Moscow (1964); English transl., MIT Press, Cambridge, Mass. (1966).
16. L. Hörmander, Notions of Convexity (Progr. Math., Vol. 127), Birkhäuser, Boston (1994).