This volume is a collection of papers dealing with harmonic analysis and nonlinear differential equations and stems from a conference on these two areas and their interface held in November 1995 at the University of California, Riverside, in honor of V. L. Shapiro. There are four papers dealing directly with the use of harmonic analysis techniques to solve challenging problems in nonlinear partial differential equations. There are also several survey articles on recent developments in multiple trigonometric series, dyadic harmonic analysis, special functions, analysis on fractals, and shock waves, as well as papers with new results in nonlinear differential equations. These survey articles, along with several of the research articles, cover a wide variety of applications such as turbulence, general relativity and black holes, neural networks, and diffusion and wave propagation in porous media. A number of the papers contain open problems in their respective areas.
From reaction-diffusion to spherical harmonics by V. L. Shapiro A survey of uniqueness questions in multiple trigonometric series by J. M. Ash and G. Wang A new look at some old trigonometric expansions by R. Askey Analysis results and problems related to lattice points on surfaces by J. Bourgain A semilinear wave equation with derivative of nonlinearity containing multiple eigenvalues of infinite multiplicity by J. F. Caicedo and A. Castro The structure of the solutions to semilinear equations at a critical exponent by A. L. Edelson What do the Navier-Stokes equations tell us about turbulence? by C. Foias A reminiscence and survey of solutions to a JPL coding problem by L. H. Harper Weak limit sets of differential equations by M. W. Hirsch Towards a noncommutative fractal geometry? Laplacians and volume measures on fractals by M. L. Lapidus Some remarks on global nonexistence for nonautonomous abstract evolution equations by H. A. Levine, P. Pucci, and J. Serrin Cartwright and Littlewood on Van der Pol's equation by S. L. McMurran and J. J. Tattersall One-sided resonance for a quasilinear variational problem by A. J. Rumbos and V. L. Shapiro Shock-waves in general relativity by J. A. Smoller and J. B. Temple Dyadic harmonic analysis by W. R. Wade.