Abstract
AbstractThe spectral theory on theS-spectrum was introduced to give an appropriate mathematical setting to quaternionic quantum mechanics, but it was soon realized that there were different applications of this theory, for example, to fractional heat diffusion and to the spectral theory for the Dirac operator on manifolds. In this seminal paper we introduce the harmonic functional calculus based on theS-spectrum and on an integral representation of axially harmonic functions. This calculus can be seen as a bridge between harmonic analysis and the spectral theory. The resolvent operator of the harmonic functional calculus is the commutative version of the pseudoS-resolvent operator. This new calculus also appears, in a natural way, in the product rule for theF-functional calculus.
Publisher
Springer Science and Business Media LLC
Reference37 articles.
1. Alpay, D., Colombo, F., Gantner, J., Sabadini, I.: A new resolvent equation for the S-functional calculus. J. Geom. Anal. 25, 1939–1968 (2015)
2. Alpay, D., Colombo, F., Kimsey, D.P.: The spectral theorem for quaternionic unbounded normal operators based on the $$S$$-spectrum. J. Math. Phys. 57, 023503 (2016)
3. Alpay, D., Colombo, F., Gantner, J., Sabadini, I.: The $$H^\infty $$functional calculus based on the S-spectrum for quaternionic operators and for n-tuples of noncommuting operators. J. Funct. Anal. 271, 1544–1584 (2016)
4. Alpay, D., Colombo, F., Sabadini, I.: Slice Hyperholomorphic Schur Analysis, Theory: Advances and Applications, vol. 256. Birkhäuser, Basel (2017)
5. Alpay, D., Colombo, F., Sabadini, I.: Quaternionic de Branges Spaces and Characteristic Operator Function. Briefs in Mathematics. Springer, Cham (2020)
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献