Fractional self adjoint operator Poincaré and Sobolev type inequalities

• Autorzy: Anastassiou G. A.

Identyfikatory

DOI

10.1515/fascmath-2016-0013

• Języki publikacji: EN

Abstrakty

EN

We present here many fractional self adjoint operator Poincaré and Sobolev type inequalities to various directions. Initially we give several fractional representation formulae in the self adjoint operator sense. Inequalities are based in the self adjoint operator order over a Hilbert space.

Słowa kluczowe

EN

self-adjoint operator; Hilbert space; Poincaré inequality; Sobolev inequality; fractional derivative

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2016
• Tom: Nr 57
• Strony: 5--24
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Anastassiou G. A.

• Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.

Bibliografia

• [1] Anastassiou G.A., Fractional Differentiation Inequalities, Springer, New York, 2009.
• [2] Anastassiou G.A., Intelligent Mathematics: Computational Analysis, Springer, Heidelberg, New York, 2011.
• [3] Diethelm K., The Analysis of Fractional Differential Equations, Springer, New York, 2010.
• [4] Dragomir S.S., Inequalities for functions of self adjoint operators on Hilbert spaces, ajmaa.org/RGMIA/monographs/InFuncOp.pdf, 2011.
• [5] Dragomir S., Operator inequalities of Ostrowski and Trapezoidal type, Springer, New York, 2012.
• [6] Furuta T., Mićić Hot J., Pečaric J., Seo Y., Mond-Pečaric Method in Operator Inequalities., Inequalities for Bounded Selfadjoint Operators on a Hilbert Space, Element, Zagreb, 2005.
• [7] Helmberg G., Introduction to Spectral Theory in Hilbert Space, John Wiley & Sons, Inc., New York, 1969.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.