The field of ‘generalized functions’ comprises, among others, distributions, ultradistributions, hyperfunctions and algebras of generalized functions. It has a longstanding tradition starting in the mid-twentieth century and is actively pursued by many research groups all over the world.
The field has always developed along the requirements of applications, notably in linear and nonlinear partial differential equations (generalized solutions and regularity), geometry (linear/nonlinear distributional geometry), mathematical physics (general relativity, geophysics, fluid dynamics, quantum theory), stochastic analysis (generalized stochastic processes and stochastic partial differential equations) as well as harmonic analysis, both in theoretical and numerical aspects.
This special issue on ‘Generalized Functions and Applications’ contains a selection of 11 papers of participants of the ‘International Conference of Generalized Functions’ (GF2009) held at the University of Vienna, 31 August – 4 September, 2009. It is intended to present a view on attractive current topics of research in the field.
Its scope ranges from generalized functions in elasticity, algebras of generalized functions in general relativity, generalized solutions in gas dynamics, convolution and exchange theorems for distributions, pseudodifferential operators on symplectic spaces to nonlinear regularity and structural theory of generalized functions, all in the context of applications in partial differential equations.
We remark that further contributions of participants of the conference GF2009 have been published in Volume 22, Issues 4–5 of Integral Transforms and Special Functions.
We are grateful to the Editors-in-Chief of Applicable Analysis, Robert P. Gilbert and Yongzhi Steve Xu, for giving us the opportunity to promote the active field of generalized functions and applications by publishing this special issue in Applicable Analysis. It is our hope that this special issue will further stimulate research in the field by demonstrating the broad range of applicability.