Abstract
We present an overview of some of our recent results on the existence of rays of minimal growth for elliptic cone operators and two new results concerning the necessity of certain conditions for the existence of such rays.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Agranovich and M. Vishik, Elliptic problems with a parameter and parabolic problems of general type, Russ. Math. Surveys 19 (1963), 53–159.
S. Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math. 15 (1962), 119–147.
J. Brüning and R. Seeley, The expansion of the resolvent near a singular stratum of conical type, J. Funct. Anal. 95 (1991), 255–290.
J. Cheeger, On the spectral geometry of spaces with cone-like singularities, Proc. Nat. Acad. Sci. U.S.A. 76 (1979), 2103–2106.
J. Gil, Full asymptotic expansion of the heat trace for non-self-adjoint elliptic cone operators, Math. Nachr. 250 (2003), 25–57.
J. Gil, T. Krainer, and G. Mendoza, Geometry and spectra of closed extensions of elliptic cone operators, Canad. J. Math., to appear.
J. Gil, T. Krainer, and G. Mendoza, Resolvents of elliptic cone operators, J. Funct. Anal. 241 (2006), no. 1, 1–55.
J. Gil and G. Mendoza, Adjoints of elliptic cone operators, Amer. J. Math. 125 (2003), no. 2, 357–408.
G. Grubb, Functional calculus of pseudodifferential boundary problems, Second Edition, Birkhäuser, Basel, 1996.
V. Kondrat’ev, Boundary problems for elliptic equations in domains with conical or angular points, Trans. Mosc. Math. Soc. 16 (1967), 227–313.
T. Krainer, Resolvents of elliptic boundary problems on conic manifolds, to appear in Communications in PDE.
M. Lesch, Operators of Fuchs type, conical singularities, and asymptotic methods, B.G. Teubner, Stuttgart, Leipzig, 1997.
P. Loya, On the resolvent of differential operators on conic manifolds, Comm. Anal. Geom. 10 (2002), no. 5, 877–934.
R. Melrose, Transformation of boundary value problems, Acta Math. 147 (1981), 149–236.
E. Schrohe and J. Seiler, The resolvent of closed extensions of cone differential operators, Canad. J. Math. 57 (2005), 771–811.
B.-W. Schulze, Pseudo-differential operators on manifolds with edges, in Proc. Symp. Partial Differential Equations, Holzhau 1988 (Leipzig), Teubner-Texte zur Math. Vol. 112, Teubner, 1989, 259–288.
R. Seeley, Complex powers of an elliptic operator, in Singular Integrals, Amer. Math. Soc., Providence, 1967, 288–307.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Birkhäuser Verlag Basel/Switzerland
About this chapter
Cite this chapter
Gil, J.B., Krainer, T., Mendoza, G.A. (2006). On Rays of Minimal Growth for Elliptic Cone Operators. In: Toft, J. (eds) Modern Trends in Pseudo-Differential Operators. Operator Theory: Advances and Applications, vol 172. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8116-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8116-5_2
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8097-7
Online ISBN: 978-3-7643-8116-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)