Rellich-Kondrakov Embedding of the Laplacian Resolvent on the Torus
: This paper proves that the domain of the Laplacian, on a closed Riemannian manifold, is compactly embedded in Particularly, the resolvent of the Laplacian, is shown to be compactly embedded on the torus
R. A. Adams (1975), Sobolev Spaces. Academic Press, New York.
T. Aubin (1982), Nonlinear Analysis on Manifolds. Monge-Amp re Equations. Springer-Verlag; Heidelberg.
S. Bando and H. Urakawa (1983), Generic Properties of the Eigenvalues of the Laplacian for Compact Riemannian Manifold. T hoku Math.Journ. 35, pp.155-172.
R. Camporesi (1990), Harmonic Analysis and Propagators on Homogeneous spaces. Physics Reports (Review section of Physics Letters) 196. Nos 1 2, North-Holland, pp.1-34.
I. Chavel (1984), Eigenvalues in Riemannian Geometry. Academic Press Inc; London.
A. Grigor’yam (2009), Heat Kernels and Analysis on Manifolds. Studies in Advance Mathematics. Volume 47; American Mathematical Society International Press, United States of America.
P. G´orka, H. Prado and E.G. Reyes (2011), Nonlinear equations with infinitely many derivatives. Complex Analysis and Operator Theory. 5, pp.313–323.
K. Gr chenig and T. Strohmer (2007), Pseudodifferential operators on locally compact abelian groups and Sjstrand’s symbol class. J. Reine Angew. Math. 613, pp.121-146.
P. Haj asz (1996), Sobolev spaces on an arbitrary metric space. Potential Anal. 5, no. 4, pp.403-415.
E. Hebey (1996), Sobolev Spaces on Riemannian Manifolds. Lecture Notes in Mathematics. Springer-Verlag, Heidelberg.
D. Hoffman and J. Spruck (1974), Sobolev and isoperimetric inequalities for Riemannian submanifolds, Comm. Pure Appl. Math. 27, pp.715-727
L. Omenyi (2016); Meromorphic continuation of the spectral zeta kernel. Gen. Math. Notes, Vol. 36, No. 2, pp.26-37.
J.J. Rodr guez-Vega andW. A. Z´u˜niga-Galindo (2010), Elliptic pseudodifferential equations and Sobolev spaces over p-adic fields. Pacific Journal of Mathematics Vol. 246 , No.2, pp.407-420.
M. Ruzhansky and V. Turunen (2010), Pseudo-Differential Operators and Symmetries. Background Analysis and Advanced Topics. Birkh¨auser, Basel - Boston - Berlin.
M. E. Taylor (1996), Partial Differential Equations. Vol. I. Springer-Verlag, Heidelberg.
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