most polynomial growth on every half-space Re (z)::::: c. Moreover, Op(t) depends holomorphically on t for Re t > O. General references for much of the material on the derivation of spectral functions, asymptotic expansions and analytic properties of spectral functions are A-P-S] and Sh], especially Chapter 2. To study the spectral functions and their relation to the geometry and topology of X, one could, for example, take the natural associated parabolic problem as a starting point. That is, consider the 'heat equation' (%t + p) u(x, t) = 0 { u(x, O) = Uo(x), tP which is solved by means of...
most polynomial growth on every half-space Re (z)::::: c. Moreover, Op(t) depends holomorphically on t for Re t > O. General references for much of th...
most polynomial growth on every half-space Re (z)::::: c. Moreover, Op(t) depends holomorphically on t for Re t > O. General references for much of the material on the derivation of spectral functions, asymptotic expansions and analytic properties of spectral functions are A-P-S] and Sh], especially Chapter 2. To study the spectral functions and their relation to the geometry and topology of X, one could, for example, take the natural associated parabolic problem as a starting point. That is, consider the 'heat equation': (%t + p) u(x, t) = 0 { u(x, O) = Uo(x), tP which is solved by means...
most polynomial growth on every half-space Re (z)::::: c. Moreover, Op(t) depends holomorphically on t for Re t > O. General references for much of th...
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.
Throughout Geometry, Complex Dimensions and Zeta Functions, Second Edition, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition.
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-di...
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums.
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary...
