A direct approach to the Weiss conjecture for bounded analytic semigroups

Bounit Hamid; Driouich Adberrahim; El-Mennaoui Omar

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 2, page 527-539
  • ISSN: 0011-4642

Abstract

top
We give a new proof of the Weiss conjecture for analytic semigroups. Our approach does not make any recourse to the bounded H -calculus and is based on elementary analysis.

How to cite

top

Hamid, Bounit, Adberrahim, Driouich, and Omar, El-Mennaoui. "A direct approach to the Weiss conjecture for bounded analytic semigroups." Czechoslovak Mathematical Journal 60.2 (2010): 527-539. <http://eudml.org/doc/38025>.

@article{Hamid2010,
abstract = {We give a new proof of the Weiss conjecture for analytic semigroups. Our approach does not make any recourse to the bounded $H^\{\infty \}$-calculus and is based on elementary analysis.},
author = {Hamid, Bounit, Adberrahim, Driouich, Omar, El-Mennaoui},
journal = {Czechoslovak Mathematical Journal},
keywords = {infinite dimensional systems; analytic semigroups; unbounded observation operator; admissibility; fractional power; infinite-dimensional system; analytic semigroup; unbounded observation operator; admissibility; fractional power},
language = {eng},
number = {2},
pages = {527-539},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A direct approach to the Weiss conjecture for bounded analytic semigroups},
url = {http://eudml.org/doc/38025},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Hamid, Bounit
AU - Adberrahim, Driouich
AU - Omar, El-Mennaoui
TI - A direct approach to the Weiss conjecture for bounded analytic semigroups
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 527
EP - 539
AB - We give a new proof of the Weiss conjecture for analytic semigroups. Our approach does not make any recourse to the bounded $H^{\infty }$-calculus and is based on elementary analysis.
LA - eng
KW - infinite dimensional systems; analytic semigroups; unbounded observation operator; admissibility; fractional power; infinite-dimensional system; analytic semigroup; unbounded observation operator; admissibility; fractional power
UR - http://eudml.org/doc/38025
ER -

References

top
  1. Amann, H., Linear and quasilinear Parabolic Problems. Vol. I, Birkhäuser, Basel (1995). (1995) MR1345385
  2. Arendt, W., Batty, C., Hieber, C., Neubrander, F., Vector Valued Laplace transforms and Cauchy Problems, Vol. 96 of Monographes in Mathematics. Birkäuser (2001). (2001) Zbl0978.34001
  3. Balakrishnan, A. V., 10.2140/pjm.1960.10.419, Pacific J. Math. 10 (1960), 419-437. (1960) Zbl0103.33502MR0115096DOI10.2140/pjm.1960.10.419
  4. Engel, K., On the characterization of admissible control and observation operators, Systems and Control Letters (1998), 34 225-227. (1998) Zbl0909.93034MR1637265
  5. Faming, G., Admissibility of linear systems in Banach spaces, Journal of electronic Science and Technology in China (2004), 75-78. (2004) 
  6. Gao, M. C., Hou, J. C., 10.1007/BF01225527, Integral Equations and Operator Theory 35 (1999), 53-64. (1999) MR1707930DOI10.1007/BF01225527
  7. Grabowski, P., 10.1080/00207179508921589, Internat. J. Control 62 (1995), 1163-1173. (1995) Zbl0837.93005MR1636622DOI10.1080/00207179508921589
  8. Grabowski, P., Callier, F. M., 10.1007/BF01308629, Integral Equations Operator Theory 25 (1996), 183-196. (1996) MR1388679DOI10.1007/BF01308629
  9. Haak, B., Kunstmann, P. C., 10.1137/060656139, SIAM J. Control Optimization 45 2094-2118 (2007). (2007) Zbl1126.93021MR2285716DOI10.1137/060656139
  10. Hansen, S., Weiss, G., 10.1016/0167-6911(91)90051-F, Systems Control Letters 16 219-227 (1991). (1991) MR1098682DOI10.1016/0167-6911(91)90051-F
  11. Jacob, B., Partington, J. R., 10.1007/BF01301467, Integral Equations and Operator Theory 40 (2001), 231-243. (2001) Zbl1031.93107MR1831828DOI10.1007/BF01301467
  12. Jacob, B., Partington, J. R., Pott, S., 10.1017/S0013091500001024, Proc. Edinb. Math. Soc. 45 (2002), 353-362. (2002) Zbl1176.47065MR1912645DOI10.1017/S0013091500001024
  13. Jacob, B., Zwart, H., 10.1137/S0363012903423235, SIAM J. Control Optim. 43 137-153 (2004). (2004) Zbl1101.93042MR2082696DOI10.1137/S0363012903423235
  14. Komatsu, H., 10.2140/pjm.1966.19.285, Pacific J. Math. 19 (1966), 285-346. (1966) MR0201985DOI10.2140/pjm.1966.19.285
  15. LeMerdy, C., 10.1112/S002461070200399X, J. London Math. Soc. 67 (2003), 715-738. (2003) MR1967702DOI10.1112/S002461070200399X
  16. Partington, J. R., Pott, S., Admissibility and exact observability of observation operators for semigroups, Irish Math. Soc. Bulletin 55 19-39 (2005). (2005) Zbl1159.47302MR2185647
  17. Partington, J. R., Weiss, G., Admissible observation operators for the right-shift semigroup, Mathematics of Control, Signals and Systems (2000), 13 179-192. (2000) Zbl0966.93033MR1784262
  18. Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin (1983). (1983) Zbl0516.47023MR0710486
  19. Staffans, O., Well-posed linear systems, Cambridge University press, Cambridge (2005). (2005) Zbl1057.93001MR2154892
  20. Weiss, G., Two conjectures on the admissibility of control operators, In Estimation and Control of Distributed Parameter Systems, Birkhäuser Verlag W. Desch, F. Kappel (1991), 367-378. (1991) Zbl0763.93041MR1155659
  21. Weiss, G., 10.1137/0327028, SIAM Journal Control &amp; Optimization 27 527-545 (1989). (1989) Zbl0685.93043MR0993285DOI10.1137/0327028
  22. Weiss, G., 10.1007/BF02788172, Israel J. Math. 65 17-43 (1989). (1989) MR0994732DOI10.1007/BF02788172
  23. Zwart, H., Jacob, B., Staffans, O., 10.1016/S0167-6911(02)00277-3, Systems Control Letters 48 (2003), 341-350. (2003) Zbl1157.93421MR2020649DOI10.1016/S0167-6911(02)00277-3
  24. Zwart, H. J., 10.1016/j.sysconle.2005.02.009, Systems and Control Letters 54 973-979 (2005). (2005) Zbl1129.93422MR2166288DOI10.1016/j.sysconle.2005.02.009

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.