2003
DOI: 10.1007/s00607-004-0073-3
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Factoring and Solving Linear Partial Differential Equations

Abstract: The problem of factoring a linear partial differential operator is studied. An algorithm is designed which allows one to factor an operator when its symbol is separable, and if in addition the operator has enough right factors then it is completely reducible. Since finding the space of solutions of a completely reducible operator reduces to the same for its right factors, we apply this approach and execute a complete analysis of factoring and solving a second-order operator in two independent variables. Some r… Show more

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Cited by 34 publications
(70 citation statements)
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“…In [5] we have designed an algorithm for factoring an operator P in case of symb(P ) is separable. In particular, in this case there is only a finite number (less than 2 n ) of different factorizations of P .…”
Section: Finiteness Of the Number Of Max-imal Non-holonomic Over-ideamentioning
confidence: 99%
“…In [5] we have designed an algorithm for factoring an operator P in case of symb(P ) is separable. In particular, in this case there is only a finite number (less than 2 n ) of different factorizations of P .…”
Section: Finiteness Of the Number Of Max-imal Non-holonomic Over-ideamentioning
confidence: 99%
“…Appendix in [13]) one can supposeX 1 =D x ,X 2 =D y so we obtain the complete solution of the original equation in quadratures: if for exampleLu =…”
Section: The Classical Heritage: Laplace Transformationsmentioning
confidence: 99%
“…l 2 is also invariant of operator A 3a . Let us notice that general invariant l 3 = l 3 (ω (3) ) is a function of a simple root ω (3) of the polynomial…”
Section: Hierarchy Of Invariantsmentioning
confidence: 99%
“…with p 4 , p 5 , p 6 given explicitly for ω = ω (3) . In case of all simple roots of both polynomials P 3 (z) and R 2 (z), one will get maximal number of invariants, namely 6 general invariants.…”
Section: Hierarchy Of Invariantsmentioning
confidence: 99%
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