Beyond the Spectral Theorem: Spectrally Decomposing Arbitrary Functions of Nondiagonalizable Operators
نویسندگان
چکیده
SFI Working Papers contain accounts of scienti5ic work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at SFI, inspired by an invited visit to or collaboration at SFI, or funded by an SFI grant.
منابع مشابه
Spectral Simplicity of Apparent Complexity, Part I: The Nondiagonalizable Metadynamics of Prediction
Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type of question-correlation, predictability, predictive cost, observer synchronization, and the like-induces a distinct generator class. Answers are then function...
متن کاملA Uniqueness Theorem of the Solution of an Inverse Spectral Problem
This paper is devoted to the proof of the unique solvability ofthe inverse problems for second-order differential operators withregular singularities. It is shown that the potential functioncan be determined from spectral data, also we prove a uniquenesstheorem in the inverse problem.
متن کاملError bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert spaces via a Taylor's type expansion
On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.
متن کاملA note on spectral mapping theorem
This paper aims to present the well-known spectral mapping theorem for multi-variable functions.
متن کاملA Numerical Solution of Fractional Optimal Control Problems Using Spectral Method and Hybrid Functions
In this paper, a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly. First, the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs). Then, the unknown functions are approximated by the hybrid functions, including Bernoulli polynomials and Block-pulse functions based o...
متن کامل