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35 DAV (Browse shelf) Available 10689-01

This advanced monograph investigates through a study of heat kernels the spectral properties of linear, selfadjoint elliptic differential operators and obtains pointwise bounds for associated eigenfunctions. The book is a first account of the new techniques which can be used as a result of the recent improvements in understanding of the heat kernels obtained by means of quadratic form technique and logarithmic Sobolev inequalities. In contrast to older theories the new method enables pointwise upper and lower bounds to be obtained in terms of constants which are computable and, in many cases, sharp. The adopted approach, which is entirely analytical, enables operators in divergence form with measurable second order coefficients to be dealt with in a straightforward way. ... (Zentralblatt)

Bibliogr. p. [187]-194. Index

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