Spectral theory of a hybrid class of pseudo-differential operators

References

• Hörmander L. The analysis of linear partial differential operators, III. Berlin: Springer-Verlag; 1984.
   Google Scholar
• Cappiello M, Rodino L. SG–pseudo-differential operators and Gelfand-Shilov spaces. Rocky mountain. J. Math. 2006;36:1117–1148.
   Web of Science ®Google Scholar
• Cataňa V. M-Hypoelliptic pseudo-differential opeartors on Lp(ℝn). Appl. Anal. 2008;87:657–666.
   Web of Science ®Google Scholar
• Cordes HO. A global parametrix for pseudodifferential operators over ℝⁿ, with applications, preprint. Vol. 90. Bonn: SFB 72; 1976.
   Google Scholar
• Parenti C. Operatori pseudodifferenziali in ℝn e applicazioni. Ann. Math. Pura Appl. 1972;93:359–389.
   Google Scholar
• Schrohe E. 1986. Spaces of weighted symbols and weighted Sobolev spaces on Manifolds. In: Cordes HO, Gramsch B, Widom H, editors. Proceeding Oberwolfach, No 1256. New York: Springer LNM. p. 360–377.
   Google Scholar
• Erkip AK, Schrohe E. Normal solvability of elliptic boundary value problems on asymptotically falt manifolds. J. Func. Anal. 1992;109:22–51.
   Web of Science ®Google Scholar
• Melrose R. Spectral and scattering theory for Laplacian on asymptotically Euclidean spaces. In: Taft E, Nashed Z, editors. Spectral and scattering theory (Sanda, 1992). 161. Lecture notes in Pure and Apll. Math. New york: Deker; 1994. p. 85–130.
   Google Scholar
• Cordes HO. The thechnique pseudodifferential operators. Cambridge (UK): London Mathematical Society Lecture Notes/Cambridge Univ. Press; 1995. p. 202.
   Google Scholar
• Shubin MA. Pseudodifferential operators and spectral theory. Berlin: Springer-Verlag; 1987.
   Google Scholar
• Shubin MA. Pseudodifferential operators on ℝn. Sov. Math. Dokl. 1987;12:147–151.
   Google Scholar
• Schulze BW. Pseudodifferential boundary value problem, conical singularities and asymtotics. Berlin: Akademie-Verlag; 1994.
   Google Scholar
• Egorov Y, Schulze BW. Pseudodifferential operators, singularities, applications. Basel (Switzerland): Birkhäuser; 1997.
   Google Scholar
• Witt I. A calculus for classical pseudodifferential operators with non-smooth symbols. Math. Nachr. 1998;194:239–284.
   Web of Science ®Google Scholar
• Coriasco S, Panarese P. Fourier integral operators defined by classical symbols with exit behaviour. Math. Nachr. 2002;242:61–78.
   Web of Science ®Google Scholar
• Coriasco S. Fourier integral operators in SG classes I: Composition theorems and action on SG Sobolev spaces. Rend. Sem. Mat. Univ. Politec. Torino (1999). 2002;57: 249–302.
   Google Scholar
• Coriasco S. Fourier integral operators in SG classes II: Application to hyperbolic to Cuachy problems. An. Univ. Ferrara Sez. VII Sc. Mat. 1998;44:81–122.
   Google Scholar
• Andrews GD. A closed class of SG Fourier integral operators with applications [PhD thesis]. London: Imperial College; 2004.
   Google Scholar
• Ruzhansky M, Sugimoto M. Global L2boundedness theorems for a class of Fourier integral operators. Comm. Partial Differentiao Eduqations. 2006;31:547–569.
   Web of Science ®Google Scholar
• Coriasco S. On the boundedness of Fourier integral operators on Lp(ℝn). C. R. Acad. Sci. Paris, Ser. I. 2010;348:847–851.
   Google Scholar
• Coriasco S, Ruzhansky M. Global Lpcontinuity of Fourier integral operators, arXive;0910.2751. Trans. Amer. Math. Sco. 2012.
   Google Scholar
• Coriasco S, Maniccia L. Wave-front set at infinity and hyperbolic Linear Operators with Multiple characteristics. Ann. Global. Anal. Geom. 2003;24:375–400.
   Web of Science ®Google Scholar
• Coriasco S, Hohansson K, Toft J. Global Wave-front sets of Banach, Frěchet and Modulation space type, and pseudodifferential operators. J. Differ. Equations. 2013;254:3228–3258.
   Web of Science ®Google Scholar
• Coriasco S, Schulz R. The global wave-front set of tempered oscillatory integrals with inhomogeneous phase functions. J. Forier Anal. Appl;2013;19:1093–1121.
   Google Scholar
• Maniccia L, Schrohe E, Seiler J. Determinants of classical SG–pseudo-differential operators Preprint. http://www.ifam.uni-hannover.de/seiler/artikel/ifam86.pdf.
   Google Scholar
• Maniccia L, Schrohe E, Seiler J. Complex power of classical SG pseudodifferential operators. Ann. Univ. Ferrara Sez. VII Sc. Mat. 2006;52:353–369.
   Google Scholar
• Maniccia L, Panarese P. Egienvalue asymptotics for a class of md- elliptic ψdo’s on manifolds with cylindrical exits. Ann. Mat. Pura Appl. (4). 2002;181:283–308.
   Google Scholar
• Nicola F. Trace functionals for a class of pseudo-differential operators in ℝn. Math. phys. Anal. Geom. 2003;6:89–105.
   Web of Science ®Google Scholar
• Battisti U, Coriasco S. Wodzicki residue for operators on manifolds with cylindrical ends. Ann. Global Anal. Geom. 2011;40:223–249.
   Web of Science ®Google Scholar
• Coriasco S, Maniccia L. On the spectral asymptotics of operators on manifold with ends. Abstr. Appl. Anal. 2013;2013:1–21.
   Web of Science ®Google Scholar
• Boggiatto P, Buzano E, Rodino L. Global hypoellipticity and spectral theory. Berlin (Germany)Akademie-Verlag; 1996.
   Google Scholar
• Nicola F, Rodino L. SG pseudo-differential operators and weak hyperbolicity. Pliska Stud. Math. Bulgar. 2002;15:5–19.
   Google Scholar
• Dasgupta A, Wong MW. Spectral theory of SG-pseudo-differential opearors on Lp(ℝn). Studia Math. 2008;187:185–197.
   Web of Science ®Google Scholar
• Garello G, Morando A. A class of Lp bounded pseudo-differential operators, in Progress in Analysis. In: Begeher HGW, Gilbert RP, Wong MW, editors. Vol. I. Singapore: World scientific; 2003. p. 689–696.
   Google Scholar
• Ruzhansky M, Turunen V. Pseudo-differential operators and symmetries. Basel (Switzerland): Birkhäuser; 2009.
   Google Scholar
• Taylor ME. Pseudo-differential operators. Princton: Princton University Press; 1981.
   Google Scholar
• Wong MW. An introduction to pseudo-differential operators. 2nd ed. Singapore: World Scientific; 1999.
   Google Scholar
• Agmon S, Douglis A, Nirenberg L. Estimates near boundary for solusions of elliptic partial differential equations satisfying general boudary conditions. I. Comm. Pure. Appl. Math. 1959;12:623–727.
   Web of Science ®Google Scholar
• Wong MW. M-elliptric pseudo-differential operators on Lp(ℝn). Math. Nachr. 2006;279:319–326.
   Web of Science ®Google Scholar
• Schechter M. On the essential spectrum of an arbitrary operator I. J. Math. Anal. Appl. 1966;13:205–215.
   Web of Science ®Google Scholar
• Wolf F. On the essential spectrum of partial differential boundary problems. Comm. Pure Appl. Math. 1959;12:211–228.
   Web of Science ®Google Scholar
• Wong MW. Lp-spectra of strongly Carleman pseudo-differential operators. J. Fun. Anal. 1981;44:163–173.
   Web of Science ®Google Scholar
• Wong MW. Fredholm pseudo-differential operators on weighted Sobolev spaces. Ark. Mat. 1983;21:271–282.
   Web of Science ®Google Scholar
• Atkinson FV. The normal solobility of linear equations in normed spaces(Russian). Mat. Sbornik N. S. 1951;28:3–14.
   Google Scholar
• Grushin VV. Pseudo-differential operators on ℝn with bounded symbols. Fun. Anal. Appl. 1970;4:202–212.
   Google Scholar