Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T16:57:11.671Z Has data issue: false hasContentIssue false
  • English
  • Français

Geometry and Spectra of Closed Extensions of Elliptic Cone Operators

Published online by Cambridge University Press:  20 November 2018

Juan B. Gil ,
Thomas Krainer  and
Gerardo A. Mendoza
Juan B. Gil
Affiliation:
Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601-3760 email: [email protected], [email protected]
Thomas Krainer
Affiliation:
Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601-3760 email: [email protected], [email protected]
Gerardo A. Mendoza
Affiliation:
Department of Mathematics, Temple University, Philadelphia, PA 19122 email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the geometry of the set of closed extensions of index 0 of an elliptic differential cone operator and its model operator in connection with the spectra of the extensions, and we give a necessary and sufficient condition for the existence of rays of minimal growth for such operators.

Keywords

58J5035J7014M15Resolventsmanifolds with conical singularitiesspectral theoryboundary value problemsGrassmannians
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 4 , 01 August 2007 , pp. 742 - 794
Copyright
Copyright © Canadian Mathematical Society 2007

References

[1] BrÜning, J. and Seeley, R., An index theorem for first order regular singular operators. Amer. J. Math. 110(1988), no. 4, 659–714.Google Scholar
[2] Gil, J., Full asymptotic expansion of the heat trace for non-self-adjoint elliptic cone operators. Math. Nachr. 250(2003), 25–57.Google Scholar
[3] Gil, J., Krainer, T., and Mendoza, G., Resolvents of elliptic cone operators. J. Funct. Anal. 241(2006), no. 1, 1–55.Google Scholar
[4] Gil, J. and Mendoza, G., Adjoints of elliptic cone operators. Amer. J. Math. 125(2003), no. 2, 357–408.Google Scholar
[5] Lesch, M., Operators of Fuchs type, conical singularities, and asymptotic methods. Teubner-Texte zur Mathematik 136, B.G. Teubner, Stuttgart, 1997.Google Scholar
[6] Loya, P., On the resolvent of differential operators on conic manifolds. Comm. Anal. Geom. 10(2002), no. 5, 877–934.Google Scholar
[7] Melrose, R., Transformation of boundary problems. Acta Math. 147(1981), no. 3-4, 149–236.Google Scholar
[8] Melrose, R., The Atiyah-Patodi-Singer index theorem. Research Notes in Mathematics 4, A K Peters, Wellesley, MA, 1993.Google Scholar
[9] Mooers, E., Heat kernel asymptotics on manifolds with conic singularities. J. Anal. Math. 78(1999), 1–36.Google Scholar
[10] Schrohe, E. and Seiler, J., The resolvent of closed extensions of cone differential operators. Canad. J. Math. 57(2005), no. 4, 771–811.Google Scholar
[11] Schulze, B.-W., Pseudo-differential operators on manifolds with singularities. Studies in Mathematics and its Applications 24, North-Holland, Amsterdam, 1991.Google Scholar
[12] Seeley, R., Complex powers of an elliptic operator. In: Singular Integrals, American Mathematical Society, Providence, RI, 1967, pp. 288–307.Google Scholar