Ostrowski’s type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces
Archivum Mathematicum (2015)
- Volume: 051, Issue: 4, page 233-254
- ISSN: 0044-8753
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topDragomir, S.S.. "Ostrowski’s type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces." Archivum Mathematicum 051.4 (2015): 233-254. <http://eudml.org/doc/276275>.
@article{Dragomir2015,
abstract = {Some Ostrowski’s type inequalities for the Riemann-Stieltjes integral $\int _\{a\}^\{b\}f\left( e^\{it\}\right) du\left( t\right) $ of continuous complex valued integrands $f\colon \mathcal \{C\}\left( 0,1\right) \rightarrow \mathbb \{C\}$ defined on the complex unit circle $\mathcal \{C\}\left( 0,1\right) $ and various subclasses of integrators $u\colon \left[ a,b\right] \subseteq \left[ 0,2\pi \right] \rightarrow \mathbb \{C\}$ of bounded variation are given. Natural applications for functions of unitary operators in Hilbert spaces are provided as well.},
author = {Dragomir, S.S.},
journal = {Archivum Mathematicum},
keywords = {Ostrowski’s type inequalities; Riemann-Stieltjes integral inequalities; unitary operators in Hilbert spaces; spectral theory; quadrature rules},
language = {eng},
number = {4},
pages = {233-254},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Ostrowski’s type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces},
url = {http://eudml.org/doc/276275},
volume = {051},
year = {2015},
}
TY - JOUR
AU - Dragomir, S.S.
TI - Ostrowski’s type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 4
SP - 233
EP - 254
AB - Some Ostrowski’s type inequalities for the Riemann-Stieltjes integral $\int _{a}^{b}f\left( e^{it}\right) du\left( t\right) $ of continuous complex valued integrands $f\colon \mathcal {C}\left( 0,1\right) \rightarrow \mathbb {C}$ defined on the complex unit circle $\mathcal {C}\left( 0,1\right) $ and various subclasses of integrators $u\colon \left[ a,b\right] \subseteq \left[ 0,2\pi \right] \rightarrow \mathbb {C}$ of bounded variation are given. Natural applications for functions of unitary operators in Hilbert spaces are provided as well.
LA - eng
KW - Ostrowski’s type inequalities; Riemann-Stieltjes integral inequalities; unitary operators in Hilbert spaces; spectral theory; quadrature rules
UR - http://eudml.org/doc/276275
ER -
References
top- Dragomir, S. S., On the Ostrowski’s inequality for Riemann-Stieltjes integral, Korean J. Appl. Math. 7 (2000), 477–485. (2000) Zbl0969.26017
- Dragomir, S. S., On the Ostrowski inequality for Riemann-Stieltjes integral where is of Hölder type and is of bounded variation and applications, J. KSIAM 5 (1) (2001), 35–45. (2001)
- Dragomir, S. S., 10.15352/afa/1399900269, Ann. Funct. Anal. 2 (1) (2011), 139–205. (2011) Zbl1231.47012MR2811214DOI10.15352/afa/1399900269
- Dragomir, S. S., 10.1016/j.camwa.2011.10.020, Comput. Math. Appl. 62 (12) (2011), 4439–4448. (2011) Zbl1236.26016MR2855586DOI10.1016/j.camwa.2011.10.020
- Helmberg, G., Introduction to Spectral Theory in Hilbert Space, John Wiley and Sons, 1969. (1969) Zbl0177.42401MR0243367
- Ostrowski, A., 10.1007/BF01214290, erman), Comment. Math. Helv. 10 (1) (1937), 226–227. (1937) MR1509574DOI10.1007/BF01214290
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