By Klaus Kirsten
The literature at the spectral research of moment order elliptic differential operators includes a good deal of data at the spectral features for explicitly recognized spectra. an identical isn't really precise, in spite of the fact that, for events the place the spectra usually are not explicitly recognized. during the last a number of years, the writer and his colleagues have built new, cutting edge tools for the precise research of various spectral features happening in spectral geometry and less than exterior stipulations in statistical mechanics and quantum box concept. Spectral capabilities in arithmetic and Physics provides a close evaluate of those advances. the writer develops and applies tools for studying determinants coming up whilst the exterior stipulations originate from the Casimir impact, dielectric media, scalar backgrounds, and magnetic backgrounds. The zeta functionality underlies all of those recommendations, and the e-book starts off through deriving its uncomplicated homes and family members to the spectral capabilities. the writer then makes use of these family to improve and follow tools for calculating warmth kernel coefficients, useful determinants, and Casimir energies. He additionally explores purposes within the non-relativistic context, particularly utilising the ideas to the Bose-Einstein condensation of a great Bose gas.Self-contained and obviously written, Spectral services in arithmetic and Physics deals a distinct chance to obtain beneficial new options, use them in various purposes, and be encouraged to make additional advances.