Heat invariants of Riemannian manifolds
TLDR
In this article, a multidimensional generalization of the Agmon-Kannai method is presented for the computation of heat invariants of Riemannian manifolds without boundary.Abstract:
We calculate heat invariants of arbitrary Riemannian manifolds without boundary. Every heat invariant is expressed in terms of powers of the Laplacian and the distance function. Our approach is based on a multidimensional generalization of the Agmon-Kannai method. An application to computation of the Korteweg-de Vries hierarchy is also presented.read more
Citations
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Nearly Tight Frames and Space-Frequency Analysis on Compact Manifolds
Daryl Geller,Azita Mayeli +1 more
TL;DR: In this paper, the Laplace-Beltrami operator on a smooth compact oriented Riemannian manifold of dimension n without boundary has been studied, and it has been shown that the functions φ j,k ∈ Ej,k form a frame for (I − P)L2(M), for b sufficiently small (here P is the projection onto the constant functions).
Journal ArticleDOI
Continuous Wavelets on Compact Manifolds
Daryl Geller,Azita Mayeli +1 more
TL;DR: In this paper, the authors define continuous wavelets on a smooth compact oriented Riemannian manifold and characterize the Holder continuous functions on M by the size of their continuous wavelet transforms, for Holder exponents strictly between 0 and 1.
Journal ArticleDOI
Continuous Wavelets on Compact Manifolds
Daryl Geller,Azita Mayeli +1 more
TL;DR: In this paper, the Laplace-Beltrami operator on a Riemannian manifold was shown to be well-localized near the diagonal, in the sense that it satisfies estimates akin to those satisfied by the kernel of the convolution operator $f(t^2\Delta)$ on $\RR^n$.
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Laplace operators on fractals and related functional equations
TL;DR: In this article, the authors give an overview over the application of functional equations, namely the classical Poincare and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals.
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Regularized Traces and Taylor Expansions for the Heat Semigroup
Michael Hitrik,Iosif Polterovich +1 more
TL;DR: In this paper, the coefficients in asymptotics of regularized traces and associated trace distributions for Schrodinger operators with short and long range potentials are derived, and a connection with non-commutative Taylor formulas is established.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Journal ArticleDOI
Higher Transcendental Functions
TL;DR: Higher Transcendental Functions Based on notes left by the late Prof. Harry Bateman, and compiled by the Staff of the Bateman Project as discussed by the authors, are presented in Table 1.