Algebraic analysis
Technique of studying linear partial differential equations
Algebraic analysis is an area of mathematics that deals with systems of linear partial differential equations by using sheaf theory and complex analysis to study properties and generalizations of functions such as hyperfunctions and microfunctions. Semantically, algebraic analysis is the application of algebraic operations on analytic quantities.
Nº Q4723988 ★
Common · Knowledge
Algebraic analysis
Technique of studying linear partial differential equations
Algebraic analysis is an area of mathematics that deals with systems of linear partial differential equations by using sheaf theory and complex analysis to study properties and generalizations of functions such as hyperfunctions and microfunctions. Semantically, algebraic analysis is the application of algebraic operations on analytic quantities.
From Wikipedia
Algebraic analysis is an area of mathematics that deals with systems of linear partial differential equations by using sheaf theory and complex analysis to study properties and generalizations of functions such as hyperfunctions and microfunctions. Semantically, algebraic analysis is the application of algebraic operations on analytic quantities. As a research programme, it was started by the Japanese mathematician Mikio Sato in 1959. This can be seen as an algebraic geometrization of analysis. According to Schapira, parts of Sato's work can be regarded as a manifestation of Grothendieck's style of mathematics within the realm of classical analysis. It derives its meaning from the fact that the differential operator is right-invertible in several function spaces. It helps in the simplification of the proofs due to an algebraic description of the problem considered.
Text: Wikipédia, CC BY-SA 4.0. ·
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