Universal Bounds for Traces of the Dirichlet Laplace Operator

[1]  René Carmona,et al.  Can one hear the dimension of a fractal? , 1986 .

[2]  P. Lemberger.  Segregation in the Falicov-Kimball model , 1992 .

[3]  H. McKean,et al.  Curvature and the Eigenvalues of the Laplacian , 1967 .

[4]  Reinhard Racke,et al.  Elastic and electro-magnetic waves in infinite waveguides , 2008 .

[5]  P. Trillenberg,et al.  Refined asymptotic expansion for the partition function of unbounded quantum billiards , 1990 .

[6]  Ulrich Brehm,et al.  Lattice triangulations of E 3 and of the 3-torus , 2009 .

[7]  E. Lieb,et al.  On semi-classical bounds for eigenvalues of Schrödinger operators , 1978 .

[8]  T. Merkle,et al.  Conformally closed Poincaré-Einstein metrics with intersecting scale singularities , 2008 .

[9]  Rupert L. Frank,et al.  Eigenvalue estimates for Schrödinger operators on metric trees , 2007, 0710.5500.

[10]  Lance Smith,et al.  The asymptotics of the heat equation for a boundary value problem , 1981 .

[11]  E. Krahn,et al.  Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises , 1925 .

[12]  Non‐classical Eigenvalue Asymptotic for Elliptic Operators of Second Order in Unbounded Trumpet‐shaped Domains with Neumann Boundary Conditions , 1993 .

[13]  E. Davies,et al.  Trace properties of the Dirichlet Laplacian , 1985 .

[14]  M. Kac.  On Some Connections between Probability Theory and Differential and Integral Equations , 1951 .

[15]  M. Berg.  On the spectrum of the Dirichlet Laplacian for horn-shaped regions in Rn with infinite volume , 1984 .

[16]  B. Kaltenbacher,et al.  Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems , 2009 .

[17]  Wolfgang Kühnel,et al.  Hamiltonian Submanifolds of Regular Polytopes , 2008, Discret. Comput. Geom..

[18]  T. Weidl,et al.  Improved Berezin-Li-Yau inequalities with a remainder term , 2007, 0711.4925.

[19]  V. Ivrii.  Microlocal Analysis and Precise Spectral Asymptotics , 1998 .

[20]  J. Fleckinger,et al.  Heat Equation on the Triadic Von Koch Snowflake: Asymptotic and Numerical Analysis , 1995 .

[21]  A. Melas.  A lower bound for sums of eigenvalues of the Laplacian , 2002 .

[22]  Russell M. Brown.  The trace of the heat kernel in Lipschitz domains , 1993 .