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Fraktionale Operatoren in verallgemeinerten Hölder-Räumen
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ISBN10: 6630418018
ISBN13: 9786630418019
Publisher: Verlag Unser Wissen
Published: Aug 24 2026
Pages: 144
Weight: 0.44
Height: 0.34 Width: 6.00 Depth: 9.00
Language: German
ISBN13: 9786630418019
Publisher: Verlag Unser Wissen
Published: Aug 24 2026
Pages: 144
Weight: 0.44
Height: 0.34 Width: 6.00 Depth: 9.00
Language: German
Die Monografie widmet sich der Untersuchung der Abbildungseigenschaften gemischter fraktionaler Riemann-Liouville-Integrale und integraler Operatoren vom Volterra-Faltungstyp in verallgemeinerten Hölder-Räumen von Funktionen mehrerer Variablen. Es werden Fragen der Beschränktheit, Stetigkeit und des Isomorphismus dieser Operatoren in klassischen, gewichteten und verallgemeinerten Hölder-Räumen untersucht, die durch gemischte Stetigkeitsmodule definiert sind.Es werden grundlegende Informationen über Hölder-Räume, fraktionale Integral- und Differentialoperatoren sowie ein Überblick über moderne Ergebnisse der fraktionalen Analysis gegeben. Bedingungen für die Beschränktheit und Theorem über die Abbildungseigenschaften gemischter fraktionaler Riemann-Liouville-Integrale in Hölder-Räumen von Funktionen mehrerer Variablen werden abgeleitet.Für Integraloperatoren vom Volterra-Faltungstyp werden Abschätzungen gemischter Stetigkeitsmodule von Funktionsbildern etabliert, Theoreme vom Zygmund-Typ bewiesen und Ergebnisse erzielt, die die Veränderung der Glattheitseigenschaften von Funktionen unter der Wirkung von Operatoren charakterisieren. Die erhaltenen Ergebnisse können bei der Untersuchung von Integral- und fraktional-differentialen Gleichungen sowie bei Aufgaben der Funktionalanalysis und der mathematischen Physik verwendet werden.
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