nLab operational calculus

Operational methods/calculus are (systematic) methods to reduce some problems in analysis, typically solving differential equations, by reducing them to algebraic problems (and often also algebraic combinatorics). Most well known are methods involving Laplace transform and umbral calculus. Though it would fit the above description, this term usually does not refer to the theory of D-modules (where algebraic analysis is sometimes used term) nor differential algebra with Picard-Vessiot theory (wikipedia).

• wikipedia operational calculus
• Jan Mikusiński, Sur les fondements du calcul opératoire, Studia Mathematica 11 (1950) 41-70 doi
• G. Dattoli, E. Palma, , E. Sabia, K. Górska, A. Horzela, K. A. Penson, Operational versus umbral methods and the Borel transform, Int. J. Appl. Comput. Math (2017) 3: 3489 doi
• Gian-Carlo Rota, D. Kahaner, A. Odlyzko, On the foundations of combinatorial theory. VIII. Finite operator calculus, J. Math. Anal. Appl. 42 (1973), 684–760 MR345826 doi

category: analysis