algebraic analysis

noun

The study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions and certain generalisations of functions (such as hyperfunctions and microfunctions).

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Meanings

nounalgebraic analysis (uncountable)
  1. uncountablealgebraic geometryThe study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions and certain generalisations of functions (such as hyperfunctions and microfunctions).
    3 more examples

    1986, Goro Kato (translator), Masaki Kashiwara, Takahiro Kawai, Tatsuo Kimura, Foundations of Algebraic Analysis, Princeton University Press, https://books.google.com.au/books?id=qYUrDgAAQBAJ&printsec=frontcover&dq=%22algebraic+analysis%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwiK5MSlvsLsAhWXbn0KHbPuBPQQ6AEwAnoECAYQAg#v=onepage&q=%22algebraic%20analysis%22&f=false.

    In their classical work [123], Kashiwara, Kawai, and Kimura pointedly observe that the Japanese algebraic analysis is really the algebraic analysis in the tradition of Euler; we may add that what we mean by algebraic microlocal analysis is the successful attempt to adapt the methods of abstract algebraic geometry to the non-commutative setting in which the base ring is now the ring of variable coefficients^([sic]) partial differential operators.

    1999, Goro Kato, Daniele C. Struppa, Fundamentals of Algebraic Microlocal Analysis, Marcel Dekker, page v

    2008, Yoshitsugu Takei, The work of T. Kawai on exact WKB analysis, T. Aoki, H. Majima, Y. Takei, N. Tose (editors), Algebraic Analysis of Differential Equations, Springer, page 19, Thus Kawai has been engaged mainly in the research of exact WKB analysis or algebraic analysis of singular perturbation theory since 1989.

  2. uncountableUsed other than figuratively or idiomatically: see algebraic, analysis.; the use of techniques from algebra (especially elementary algebra) to analyse and solve problems.

Origin

The area of study in algebraic geometry began as a research programme, instigated in 1959 by Japanese mathematician Mikio Sato.

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Translations

French analyse algébrique
  • analyse algébriquestudy of systems of linear PDEs
Japanese 代数解析
  • 代数解析study of systems of linear PDEs
Spanish análisis algebraico
  • análisis algebraicostudy of systems of linear PDEs
Cite this entry
APA

algebraic analysis. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/algebraic%20analysis

MLA

“algebraic analysis.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/algebraic%20analysis. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “algebraic analysis,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/algebraic%20analysis.

Source: algebraic analysis on Wiktionary, CC BY-SA 4.0.