@article{5f39a452c846459c8b32e48ec53e57e4, title = "Polynomial as a new variable — A Banach algebra with a functional calculus", abstract = "Given any square matrix or a bounded operator A in a Hilbert space such that p(A) is normal (or similar to normal), we construct a Banach algebra, depending on the polynomial p, for which a simple functional calculus holds. When the polynomial is of degree d, then the algebra deals with continuous ℂd-valued functions, defined on the spectrum of p(A). In particular, the calculus provides a natural approach to deal with nontrivial Jordan blocks and one does not need differentiability at such eigenvalues.", keywords = "Functional calculus, Multicentric calculus, Polynomially normal, Removing Jordan blocks, Spectral mapping", author = "Olavi Nevanlinna", year = "2016", month = "9", day = "1", doi = "10.7153/oam-10-33", language = "English", volume = "10", pages = "567--592", journal = "OPERATORS AND MATRICES", issn = "1846-3886", publisher = "Element d.o.o.", number = "3", }