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Asymptotic Formulae in Spectral Geometry (Studies in Advanced Mathematics) by Peter B. Gilkey

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Published by Chapman & Hall/CRC .
Written in English

Subjects:

  • Applied mathematics,
  • Geometry,
  • Riemannian manifolds,
  • Geometry - Differential,
  • Mathematics,
  • Science/Mathematics,
  • Applied,
  • Mathematics / Geometry / General,
  • Differential equations,
  • Geometry - General,
  • Asymptotic theory,
  • Spectral geometry

Book details:

The Physical Object
FormatHardcover
Number of Pages312
ID Numbers
Open LibraryOL8795344M
ISBN 101584883588
ISBN 109781584883586

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  A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral Geometry collects these results and computations into one book. Written by a leading pioneer in the field, it focuses on the functorial and special cases methods of computiCited by: To date, however, there has been no unified discussion of these otic Formulae in Spectral Geometry collects these results and computations into one book. The author focuses on the functorial and special cases methods of computing asymptotic heat trace and heat content coefficients in the heat equation and introduces results. Get this from a library! Asymptotic formulae in spectral geometry. [Peter B Gilkey] -- "A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. These include not only the classical heat trace. Asymptotic Formulae in Spectral Geometry collects these results and computations into one book. Written by a leading pioneer in the field, it focuses on the functorial and special cases methods of computing asymptotic heat trace and heat content coefficients in the heat equation.

Electronic books: Additional Physical Format: Print version: Gilkey, Peter B. Asymptotic formulae in spectral geometry. Boca Raton: Chapman & Hall/CRC Press, © (DLC) (OCoLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Peter B Gilkey. 2 days ago  obtain sharp asymptotic formulas for D and consequently for spectral problems associated with (). In the case when σj ∈ Lp[0,1], j = 1,2, p > 2 one can use the results from [7] due to the obvious embedding between Lp[0,1] spaces. Thus, in this text we restrict ourselves only to 1 ≤ p spectral problem. 2 days ago  These results allows us to obtain sharp asymptotic formulas for eigenvalues and eigenfunctions of Sturm--Liouville operators associated with the aforementioned Dirac system. Subjects: Spectral Theory () MSC classes: 34L20, 34E Cite as: arXiv [] (or arXivv1 [] for this version). Another set of ideas in spectral geometry concerns with different types of trace formulae and applications to number theory, quantum physics, and quantum chaos. In some sense this even goes back to the very origins of the Weyl's law in quantum mechanics and in deriving Planck's radiation formula .

In book: Spectral Action in Noncommutative Geometry, pp in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral. The spectral theory of Sturm-Liouville operators is a classical domain of analysis, comprising a wide variety of problems. Besides the basic results on the structure of the spectrum and the eigenfunction expansion of regular and singular Sturm-Liouville problems, it is in this domain that one-dimensional quantum scattering theory, inverse spectral problems, and the surprising connections of. The book concludes with an appendix including some auxiliary tools from geometry and analysis, along with examples of spectral geometries. The book serves both as a compendium for researchers in. Spectral geometry deals with the study of the influence of the spectra of such operators on the geometry and topology of a Riemannian manifold (possibly with boundary; cf. also Spectrum of an operator). Everything started with the classical Weyl asymptotic formula, and was later translated into the colloquial question "Can one hear the shape of.