Fetching the paper…
Reading the bibliography…
In these three lectures we will discuss some fundamental aspects of the theory of self-adjoint extensions of the covariant Laplace-Beltrami and Dirac operators on compact Riemannian manifolds with smooth boundary emphasizing the relation with the theory of global boundary conditions.
H. Weyl. Über geowöhniliche lineare Differentialgleichungen mit singulären stellen und ihre Euigenfunktionen
1910
Earlier work this paper cites.
J. von Neumann. Allgemeine Eigenwerttheorie Hermitischer Funktionaloperatoren
1929
Earlier work this paper cites.
N.I. Akhiezer, I.M. Glazman. The theory of Linear Operators in Hilbert Space . Vols. I, II. Frederick Ungar Publ. N.Y. (1963)
1963
Earlier work this paper cites.
N. Dunford, J.T. Schwartz. Linear Operators, Part II: Spectral theory, self–adjoint operators in Hilbert space
1963
Earlier work this paper cites.
P.A.M. Dirac. Lectures on Quantum Mechanics . Belfer Graduate School of Science, Yeshiva Univ. NY (1964)
1964
Earlier work this paper cites.
S. Agmon. Lectures on Elliptic Boundary Value Problems . Van Nostrand Math. Stud. 2
1965
Earlier work this paper cites.
K. Yoshida. Functional Analysis
1965
Earlier work this paper cites.
V. Arnold. Characteristic classes entering in quantization conditions . Funct. Anal. Appl., 1
1967
Earlier work this paper cites.
G. Grubb. A characterization of the non-local boundary value problems associated with an elliptic operator . Ann. Scuola Norm. Sup. Pisa, 22
1968
Earlier work this paper cites.
M.A. Naimark. Linear Differential Operators
1968
Earlier work this paper cites.
J.L. Lions, E. Magenes. Non-homogeneous Boundary Value Problems and Applications
1972
Earlier work this paper cites.
E.A. Coddington. Extension theory of formally normal and symmetric subspaces
1973
Earlier work this paper cites.
R.A. Adams. Sobolev Spaces . Academic Press NY (1975)
1975
Earlier work this paper cites.
M. Reed, B. Simon. Methods of modern mathematical physics II: Fourier transform and self–adjointness
1975
Earlier work this paper cites.
M.F. Atiyah, V.K. Patodi, I.M. Singer. Spectral asymmetry and Riemannian Geometry I, II and III. Math. Proc. Camb. Phil. Soc., 77
1976
Cited alongside, same era.
J. Weidmann. Linear Operators in Hilbert Spaces
1980
Cited alongside, same era.
S. Rempel, B.-W. Schulze. Index Theory of Elliptic Boundary Problems
1985
Cited alongside, same era.
G. Segal, G. Wilson. Loop Groups and Equations of KdV Type
1985
Cited alongside, same era.
A. Pressley, G. Segal. Loop Groups
1986
Cited alongside, same era.
E. Witten. Quantum Field Theory, Grassmannians, and Algebraic Curves
1988
Cited alongside, same era.
V. John, G. Jungman, S. Vaidya. The Renormalization Group and Quantum Hall Edge States . Nucl. Phys. B, 455
1995
Later among the works it cites.
G. Grubb. Functional calculus of pseudodifferential boundary problems . 2nd ed. Progress in Mathematics (Boston, Mass.). 65. Basel: Birkhäuser. viii, 522 (1996)
1996
Later among the works it cites.
L. Friedlander, A. Schwarz. Grassmannian and Elliptic Operators . ArXiv: funct-an/9704003 (1997)
1997
Later among the works it cites.
G. Grubb. Trace expansions for pseudodifferential boundary problems for Dirac–type operators and more general systems . Arkiv f. Matematik, 37
1999
Later among the works it cites.
G. Grubb. Spectral boundary conditions for generalizations of Laplace and Dirac operators . Commun. Math. Phys., 240
2003
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
H. B. Lawson, M.-L. Michelsohn. Spin Geometry , Princeton Univ. Press, Princeton, New Jersey (1989)
1989
Cited alongside, same era.
B. Booß-Bavnbek, K. P. Wojciechowski. Elliptic Boundary Problems for Dirac Operators . Birkhäuser, Boston (1993)
1993
Cited alongside, same era.
J.W. Robbin, D.A. Salamon. The Maslov index for paths
1993
Cited alongside, same era.
X. Dai, D.S. Freed. η \eta –invariants and Determinant Lines . J. Math. Phys., 35
1994
Cited alongside, same era.
A.P. Balachandran, G. Bimonte, G. Marmo, A. Simoni. Topology change and Quantum Physics . Nucl. Phys., B446
1995
Cited alongside, same era.
I.L. Egusquiza. Self–adjoint extensions and signature change Class. Quantum Grav., 12
1995
Cited alongside, same era.
M. Asorey, A. Ibort, G. Marmo. Global Theory of Quantum Boundary Conditions and Topology Change . Int. J. Mod. Phys. A20
2005
Later among the works it cites.
C. Frey. On Non–local Boundary Value Problems for Elliptic Operators . Ph. D. Dissertation. Univ. Köln (2005)
2005
Later among the works it cites.
G. Grubb. Analysis of invariants associated with spectral boundary problems for elliptic operators . In Spectral geometry of manifolds with boundary and decomposition of manifolds, vol. 366
2005
Later among the works it cites.
M. Asorey, J.M. Muñoz–Casteñeda. Vacuum boundary effects . J. Phys. A: Math. Theor. 41
2008
Later among the works it cites.
J. Brüning, V. Geyler, K. Pankrashkin. Specrtra of self–adjoint extensions and applications to solvable Schrödinger operators . Rev. Math. Phys., 20
2008
Later among the works it cites.
M. V. Berry, M.R. Dennis. Boundary–condition–varying circle billiards and gratins: the Dirichlet singularity
2009
Later among the works it cites.
2011
Later among the works it cites.
A. Ibort, F. Lledó, J.M. Pérez–Pardo. On the theory of self–adjoint extensions of the Laplace–Beltrami operator and quadratic forms . In preparation (2012)
2012
Closest in time.