Spectral Functions in Mathematics and Physics by Klaus Kirsten

The literature at the spectral research of moment order elliptic differential operators encompasses a good deal of knowledge at the spectral services for explicitly identified spectra. an identical isn't precise, notwithstanding, for occasions the place the spectra aren't explicitly recognized. during the last a number of years, the writer and his colleagues have constructed new, cutting edge equipment for the precise research of numerous spectral features taking place in spectral geometry and lower than exterior stipulations in statistical mechanics and quantum box concept.

Spectral features in arithmetic and Physics provides a close review of those advances. the writer develops and applies equipment for examining determinants coming up whilst the exterior stipulations originate from the Casimir influence, dielectric media, scalar backgrounds, and magnetic backgrounds. The zeta functionality underlies all of those recommendations, and the ebook starts off through deriving its easy homes and family to the spectral services. the writer then makes use of these kin to improve and follow equipment for calculating warmth kernel coefficients, sensible determinants, and Casimir energies. He additionally explores purposes within the non-relativistic context, specifically employing the thoughts to the Bose-Einstein condensation of a terrific Bose gas.

Self-contained and obviously written, Spectral features in arithmetic and Physics bargains a special chance to obtain necessary new recommendations, use them in numerous functions, and be encouraged to make extra advances.