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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.52 no.1 Bogotá Jan./June 2018
https://doi.org/10.15446/recolma.v51n2.74529
Original articles
Orthogonal Decomposition in Omega-Weighted Classes of Functions Subharmonic in the Half-Plane
Descomposición ortogonal de funciones subharmónicas en el semiplano por medio de clases omega-pesadas
1 Universidad de Antioquia, Medellín - Colombia
2 Universidad de Antioquia, Medellín - Colombia
The paper gives a harmonic, (-weighted, half-plane analog of W. Wirtinger's projection theorem and its (1-r)(-weighted extension by M. Djrbashian and also an orthogonal decomposition for some classes of functions subharmonic in the half-plane.
Keywords: Subharmonic functions; orthogonal decomposition; potentials
El artículo da un análogo armónico (-pesado en el semiplano del teorema de proyección de W. Wirtinger y su extensión (1-r)(-pesada establecida por M. Djrbashian. También es hallada una descomposición ortogonal para algunas clases de funciones subarmónicas en el semiplano.
Palabras clave: Funciones subarmónicas; descomposición ortogonal; potenciales
References
1. Djrbashian, M., On the representability problem of analytic functions, Soobsch. Inst. Matem. i Mekh. Akad. Nauk Arm. SSR 2 (1948). [ Links ]
2. Jerbashian, A., Functions of a-Bounded Type in the Half-Plane, Advances in Complex Analysis and Applications, Springer, 2005. [ Links ]
3. Jerbashian, A., On Ap (,( Spaces in the Half-Plane, in: Operator Theory: Advances and Applications 158 (2005), 141-158, Birkhäuser Verlag, Basel/Switzerland. [ Links ]
4. Jerbashian, A., Orthogonal decomposition of functions subharmonic in the unit disc, in: Operator Theory: Advances and Applications 190 (2009), 335-340, Birkhäuser Verlag, Basel/Switzerland. [ Links ]
5. Jerbashian, A. and Jerbashian, V., Functions of (-bounded type in the half-plane, Calculation Methods and Function Theory (CMFT) 7 (2007), no. 2, 205-238. [ Links ]
6. Koosis, P., Introduction to Hp spaces, Cambridge University Press, 1998. [ Links ]
7. Walsh, J., Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc. Coll. Publ. XX, Edwards Brothers, Inc., Ann Arbor, Michigan, 1956. [ Links ]
8. Wirtinger, W., Über eine Minimumaufgabe im Gebiet der analytischen Functionen, Monatshefte für Math. und Phys. 39 (1932). [ Links ]
Received: April 01, 2017; Accepted: December 06, 2017