✦ LIBER ✦

FFT-like Multiplication of Linear Differential Operators

✍ Scribed by Joris Van Der Hoeven

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 214 KB
Volume: 33
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.2000.0496

No coin nor oath required. For personal study only.

✦ Synopsis

It is well known that integers or polynomials can be multiplied in an asymptotically fast way using the discrete Fourier transform. In this paper, we give an analogue of fast Fourier multiplication in the ring of skew polynomials C[x, δ], where δ = x ∂ ∂x . More precisely, we show that the multiplication problem of linear differential operators of degree n in x and degree n in δ can be reduced to the n×n matrix multiplication problem.

📜 SIMILAR VOLUMES

Weyl Closure of a Linear Differential Op

Weyl Closure of a Linear Differential Operator

✍ Harrison Tsai 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 382 KB

We study the Weyl closure Cl(L) = K(x) ∂ L ∩ D for an operator L of the first Weyl algebra D = K x, ∂ . We give an algorithm to compute Cl(L) and we describe its initial ideal under the order filtration. Our main application is an algorithm for constructing a Jordan-Hölder series for a holonomic D-m

OnLp-Contractivity of Semigroups Generat

OnLp-Contractivity of Semigroups Generated by Linear Partial Differential Operators

✍ Mikael Langer; Vladimir Maz'ya 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 236 KB

This paper is devoted to the study of contraction semigroups generated by linear partial differential operators. It is shown that linear partial differential operators of order higher than two cannot generate contraction semigroups on (L p ) N for p # [1, ) unless p=2. If p>1 and the L p -dissipativ

Some Necessary Conditions for Local Solv

Some Necessary Conditions for Local Solvability of Linear Partial Differential Operators

✍ C. Shangbin 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 326 KB

Overdetermined Systems of Linear Partial

Overdetermined Systems of Linear Partial Differential Operators with Normal Principal Symbols

✍ J. Zweibel 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 277 KB

Elliptic complexes, made up of certain linear partial differential operators D 1 , ..., D d with C coefficients, are constructed. The local solvability problem for the nonhomogeneous equations D p u= f ( p # [1, ..., d]) and the local integrability problem for the homogeneous equation D 1 u=0 are so

Groups of Weighted Translation Operators

Groups of Weighted Translation Operators in Lp and Linear Nonautonomous Differential Equations

✍ B. Aulbach; N. Vanminh; P.P. Zabreiko 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 333 KB

Hyers–Ulam stability of linear different

Hyers–Ulam stability of linear differential operator with constant coefficients

✍ Takeshi Miura; Shizuo Miyajima; Sin–Ei Takahasi 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 132 KB

## Abstract Let __P__(__z__) be a polynomial of degree __n__ with complex coefficients and consider the __n__–th order linear differential operator __P__(__D__). We show that the equation __P__(__D__)__f__ = 0 has the Hyers–Ulam stability, if and only if the equation __P__(__z__) = 0 has no pure im