Iterates of operators and Gelfand–Shilov classes

References

• Baouendi , M. S. and Goulaouic , C. 1972 . Régularité analytique et itérés d'opérateurs elliptiques dégeénérés: Applications . J. Funct. Anal. , 9 : 208 – 248 .
   Google Scholar
• Baouendi , M. S. and Metivier , G. 1982 . Analytic vectors of hypoelliptic operators of principal type . Am. J. Math. , 104 : 237 – 320 .
   Web of Science ®Google Scholar
• Biagioni , H. A. and Gramchev , T. 2003 . Fractional derivative estimates in Gevrey spaces, global regularity and decay for solutions to semilinear equations in ℝ n . J. Differential Equations , 194 : 140 – 165 .
   Web of Science ®Google Scholar
• Boggiatto , P. , Buzano , E. and Rodino , L. 1996 . Global Hypoellipticity and Spectral Theory , Berlin : Akademie Verlag .
   Google Scholar
• Bolley , P. , Camus , J. and Rodino , L. 1987 . Hypoellipticité analytique-Gevrey et itérés d'opérateurs . Rend. Sem. Mat. Univ. Politec. Torino , 45 ( 3 ) : 1 – 61 .
   Google Scholar
• Bouzar , C. and Chaili , R. 2002 . Vecteurs Gevrey d'opérateurs différentiels quasihomogènes . Bull. Belg. Math. Soc. Simon Stevin , 9 ( 2 ) : 299 – 310 .
   Google Scholar
• Calvo , D. and Hakobyan , G. H. 2005 . Multi-anisotropic Gevrey regularity and iterates of operators with constant coefficients . Bull. Belg. Math. Soc. Simon Stevin , 12 ( 3 ) : 461 – 474 .
   Web of Science ®Google Scholar
• Calvo , D. and Rodino , L. 2009 . Gelfand–Shilov classes of multi-anisotropic type . Funct. Approx. Comment. Math. , 40 : 297 – 307 . Part 2
   Google Scholar
• Cappiello , M. , Gramchev , T. and Rodino , L. 2006 . Super-exponential decay and holomorphic extensions for semilinear equations with polynomial coefficients . J. Funct. Anal. , 237 : 634 – 654 .
   Web of Science ®Google Scholar
• Chung , J. , Chung , S. y. and Kim , D. 1996 . Characterization of the Gelfand–Shilov spaces via Fourier transforms . Proc. Amer. Math. Soc , 124 ( 7 ) : 2101 – 2108 .
   Web of Science ®Google Scholar
• Gelfand , I. M. and Shilov , G. E. 1968 . Generalized Functions II , New York : Academic Press .
   Google Scholar
• Gramchev , T. , Pilipovic , S. and Rodino , L. 2009 . Classes of degenerate elliptic operators in Gelfand–Shilov spaces . Oper. Theory Adv. Appl. , 189 : 15 – 31 .
   Google Scholar
• Gröchenig , K. and Zimmermann , G. 2004 . Spaces of test functions via the STFT . J. Funct. Spaces Appl , 2 ( 1 ) : 24 – 53 .
   Google Scholar
• Komatsu , H. 1962 . A proof of Kotake and Narasimhan's theorem . Proc. Japan Acad , 3 ( 9 ) : 615 – 618 .
   Google Scholar
• Kotake , T. and Narasimhan , N. S. 1962 . Fractional powers of a linear elliptic operator . Bull. Soc. Math. France , 90 : 449 – 471 .
   Google Scholar
• Mitijagin , B. S. 1970 . Nuclearity and Other Properties of Spaces of Type S , 45 – 49 . Providence, RI : American Mathematical Society . American Mathematical Society Translation Series 2, Vol. 93
   Google Scholar
• Pilipovic , S. 1988 . Tempered ultradistributions . Boll. Unione Mat. Ital. VII Ser. B , 2 ( 2 ) : 235 – 251 .
   Google Scholar
• Pilipovic , S. and Teofanov , N. 2004 . Pseudodifferential operators on ultramodulation spaces . J. Funct. Anal. , 208 : 194 – 228 .
   Web of Science ®Google Scholar
• Rodino , L. 1993 . Linear Partial Differential Operators in Gevrey Spaces , Singapore : World Scientific .
   Google Scholar
• Shubin , M. 1987 . Pseudodifferential Operators and the Spectral Theory , Springer Series in Soviet Mathematics Berlin : Springer-Verlag .
   Google Scholar
• Teofanov , N. 2006 . “ Ultradistributions in time–frequency analysis ” . In Operator Theory: Advances and Applications , Edited by: Boggiatto , P. , Rodino , L. , Toft , J. and Wong , M. W. 223 – 242 . Basel : Birkhäuser .
   Google Scholar
• Zanghirati , L. 1981 . Iterati di operatori quasi-ellittici e classi generalizzate di Gevrey . Boll. Unione Mat. Ital. , 18-B ( 5 ) : 411 – 428 .
   Google Scholar