Book Review: Foundations of algebraic analysis
J. L. Brylinsky · Bulletin of the American Mathematical Society · 1988
Algebraic analysis" is a term coined by Mikio Sato.It encompasses a variety of algebraic methods to study analytic objects; thus, an "algebraic analyst" would establish some properties of a function or a distribution by investigating some linear partial differential operators which annihilate it.Here is a concrete example: let ƒ be a polynomial in n complex variables Xi,X2,..., x n ; if s is a complex number, with Re(s) > 0, |ƒ| s is a well-defined continuous function on C n .Bernstein [2] showed that \f\ s extends to a meromorphic function of s with values in distributions on C n .The key step is the abstract derivation of the following equation: (B-S) F ( x , 5 ,|-,^, /r=6(s ).| /r2 ,