Author:
Felke Yonas Eshetu,Mengestie Tesfa,Takele Mollalgn Haile
Abstract
AbstractWe follow several approaches in nonlinear spectral theory and determine the various spectral forms for the nonlinear weighted superposition operator on Fock spaces. The results show that most of the forms introduced so far coincide and contain singeltons. The classical, asymptotic, and connected eigenvalues, and some numerical ranges of the operator are also identified. We further prove that the operator is both linear and odd asymptotically with respect to the pointwise multiplication operator on the spaces.
Funder
Western Norway University Of Applied Sciences
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference23 articles.
1. Alvarez, V., Márquez, M., Vukotić, D.: Superposition operators between the Bloch space and Bergman spaces. Ark. Mat. 42, 205–216 (2004)
2. Appell, J., Zabrejko, P.: Nonlinear Superposition Operators. Cambridge University Press, Cambridge (1990)
3. Appell, J., De, E., Vignoli, A.: Nonlinear Spectral Theory. de Gruyter, Berlin (2004)
4. Bonet, J., Vukotić, D.: Superposition operators between weighted Banach spaces of analytic functions of controlled growth. Monatsh Math. 170, 311–323 (2013)
5. Buckley, S., Fernández, J., Vukotic, D.: Superposition operators on Dirichlet type spaces: Papers on analysis: a volume dedicated to Olli Martio on the coccasion of his 60th birthday, in: Rep. Univ. Jyväskylä Dep. Math. Stat., vol. 83, 41–61. Univ. Jyväskylä, Jyväskylä (2001)