| Title:
|
An example of a positive semidefinite double sequence which is not a moment sequence (English) |
| Author:
|
Bisgaard, Torben Maack |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
273-277 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The first explicit example of a positive semidefinite double sequence which is not a moment sequence was given by Friedrich. We present an example with a simpler definition and more moderate growth as $(m, n) \rightarrow \infty $. (English) |
| Keyword:
|
double sequence |
| Keyword:
|
positive definite |
| Keyword:
|
moment sequence |
| MSC:
|
43A35 |
| MSC:
|
44A60 |
| idZBL:
|
Zbl 1080.43500 |
| idMR:
|
MR2059249 |
| . |
| Date available:
|
2009-09-24T11:12:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127886 |
| . |
| Reference:
|
[1] C. Berg, J. P. R. Christensen and C. U. Jensen: A remark on the multidimensional moment problem.Math. Ann. 243 (1979), 163–169. MR 0543726, 10.1007/BF01420423 |
| Reference:
|
[2] C. Berg, J. P. R. Christensen and P. Ressel: Harmonic Analysis on Semigroups.Springer-Verlag, Berlin, 1984. MR 0747302 |
| Reference:
|
[3] T. M. Bisgaard: On the growth of positive definite double sequences which are not moment sequences.Math. Nachr. 210 (2000), 67–83. Zbl 0953.43004, MR 1738938, 10.1002/(SICI)1522-2616(200002)210:1<67::AID-MANA67>3.0.CO;2-N |
| Reference:
|
[4] T. M. Bisgaard and P. Ressel: Unique disintegration of arbitrary positive definite functions on $*$-divisible semigroups.Math. Z. 200 (1989), 511–525. MR 0987584, 10.1007/BF01160953 |
| Reference:
|
[5] J. Friedrich: A note on the two-dimensional moment problem.Math. Nachr. 121 (1985), 285–286. Zbl 0578.44006, MR 0809325, 10.1002/mana.19851210118 |
| Reference:
|
[6] H. L. Hamburger: Über eine Erweiterung des Stieltjesschen Momentenproblemes.Math. Ann. 81, 82 (1920, 1921), 235–319, 120–164, 168–187. |
| Reference:
|
[7] Y. Nakamura and N. Sakakibara: Perfectness of certain subsemigroups of a perfect semigroup.Math. Ann. 287 (1990), 213–220. MR 1054564, 10.1007/BF01446888 |
| Reference:
|
[8] K. Schmüdgen: An example of a positive polynomial which is not a sum of squares of polynomials. A positive, but not strongly positive functional.Math. Nachr. 88 (1979), 385–390. MR 0543417, 10.1002/mana.19790880130 |
| . |
