2010/03/21 by А. Б. Александров, Aleksei Aleksandrov, Aleksandrov, Aleksei +2 · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.CA #math.CV #math.FA #math.SP
paper · pdf · doi:10.48550/arxiv.1003.3982
34 pages
arxiv created 2010/03/21 · openalex publication_date 2010/03/21 · arxiv updated 2010/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a continuation of our papers \citeAP2 and \citeAP3. In those papers we obtained estimates for finite differences (\DKf)(A)=f(A+K)-f(A) of the order 1 and (\DKmf)(A)\df∑j=0m(-1)m-j(m\j)f(A+jK) of the order m for certain classes of functions f, where A and K are bounded self-adjoint operator. In this paper we extend results of \citeAP2 and \citeAP3 to the case of unbounded self-adjoint operators A. Moreover, we obtain operator Bernstein type inequalities for entire functions of exponential type. This allows us to obtain alternative proofs of the main results of \citeAP2. We also obtain operator Bernstein type inequalities for functions of unitary operators. Some results of this paper as well as of the papers \citeAP2 and \citeAP3 were announced in \citeAP1.