| 1. |
|
|
| 2. |
- Bennewitz, Christer, et al.
(författare)
-
A limit point criterion with applications to nonselfadjoint equations
- 2002
-
Ingår i: Journal of Computational and Applied Mathematics. - 0377-0427. ; 148:1, s. 257-265
-
Tidskriftsartikel (refereegranskat)abstract
- A unified approach is given which allows one to construct examples of all three cases resulting from a generalization of the classical Weyl limit point limit circle analysis, for differential equations as well as for difference equations.
|
|
| 3. |
|
|
| 4. |
|
|
| 5. |
- Bennewitz, Christer, et al.
(författare)
-
A uniqueness result for one-dimensional inverse scattering
- 2012
-
Ingår i: Mathematische Nachrichten. - : Wiley. - 0025-584X. ; 285:8-9, s. 941-948
-
Tidskriftsartikel (refereegranskat)abstract
- We consider the whole-line inverse scattering problem for Sturm-Liouville equations which have constant coefficients on a half-line. Since in this case the reflection coefficient determines a Weyl-Titchmarsh m-function, it determines the coefficients up to some simple Liouville transformations. Given inverse spectral theory, proofs are fairly simple but provide extensions of known results as we require less smoothness and less decay than is customary.
|
|
| 6. |
|
|
| 7. |
- Bennewitz, Christer, et al.
(författare)
-
Approximation numbers of Sobolev embedding operators on an interval
- 2004
-
Ingår i: Journal of the London Mathematical Society. - 0024-6107. ; 70, s. 244-260
-
Tidskriftsartikel (refereegranskat)abstract
- Consider the Sobolev embedding operator from the space of functions in W-1,W-p(I) with average zero into L-p, where I is a finite interval and p > 1. This operator plays an important role in recent work. The operator norm and its approximation numbers in closed form are calculated. The closed form of the norm and approximation numbers of several similar Sobolev embedding operators on a finite interval have recently been found. It is proved in the paper that most of these operator norms and approximation numbers on a finite interval are the same.
|
|
| 8. |
- Bennewitz, Christer
(författare)
-
Approximation numbers = singular values
- 2007
-
Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427. ; 208:1, s. 102-110
-
Tidskriftsartikel (refereegranskat)abstract
- This paper introduces a generalisation of the notion of singular value for Hilbert space operators to more general Banach spaces. It is shown that for a simple integral operator of Hardy type the singular values are the eigenvalues of a non-linear Sturm-Liouville equation and coincide with the approximation numbers of the operator. Finally, asymptotic formulas for the singular numbers are deduced. (c) 2006 Published by Elsevier B.V.
|
|
| 9. |
- Bennewitz, Christer, et al.
(författare)
-
Computation of the M matrix for fourth-order problems
- 1996
-
Ingår i: Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences. - 1364-5021. ; 452:1951, s. 1765-1788
-
Tidskriftsartikel (refereegranskat)abstract
- This paper is concerned with the numerical computation of the Titchmarsh-Weyl M matrix. We show how an algorithm may be developed which relates solutions of an initial-value problem to an approximation of the M matrix. In some special cases we compare the results from our algorithm with results obtained using special functions.
|
|
| 10. |
|
|
