Name
Abstract | ||
|---|---|---|
Let T,U be two linear operators mapped onto the function f such that U(T(f))=f, but T(U(f))f. In this paper, we first obtain the expansion of functions T(U(f)) and U(T(f)) in a general case. Then, we introduce four special examples of the derived expansions. First example is a combination of the Fourier trigonometric expansion with the Taylor expansion and the second example is a mixed combination of orthogonal polynomial expansions with respect to the defined linear operators T and U. In the third example, we apply the basic expansion U(T(f))=f(x) to explicitly compute some inverse integral transforms, particularly the inverse Laplace transform. And in the last example, a mixed combination of Taylor expansions is presented. A separate section is also allocated to discuss the convergence of the basic expansions T(U(f)) and U(T(f)). |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.cam.2009.12.030 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
inverse laplace,basic expansion,new expansion,linear operator,last example,fourier trigonometric expansion,taylor expansion,special example,mixed combination,orthogonal polynomial expansion,general case,functional equation,inverse laplace transform,functional equations,orthogonal polynomial,integral transforms | Laplace transform,Recurrence relation,Mathematical analysis,Linear map,Taylor expansions for the moments of functions of random variables,Functional equation,Integral transform,Inverse Laplace transform,Mathematics,Taylor series | Journal |
Volume | Issue | ISSN |
234 | 2 | 0377-0427 |
Citations | PageRank | References |
1 | 0.38 | 1 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mohammad Masjed-Jamei | 1 | 15 | 8.03 |