Functions of perturbed unbounded self-adjoint operators. Operator bernstein type inequalities

Standard

Functions of perturbed unbounded self-adjoint operators. Operator bernstein type inequalities. / Александров, Алексей Борисович ; Peller, V. V.

In: Indiana University Mathematics Journal, Vol. 59, No. 4, 2010, p. 1451-1490.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{c729482b744d49469ed483c075f17828,

title = "Functions of perturbed unbounded self-adjoint operators. Operator bernstein type inequalities",

abstract = "This is a continuation of our papers [3] and [4]. In those papers we obtained estimates for finite differences (δkf) (A) = f(A + K) -f(A) of the order 1 and mathematcal equation represented of the order m for certain classes of functions f , where A and K are bounded self-adjoint operators. In this paper we extend results of [3] and [4] 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 [3]. We also obtain operator Bernstein type inequalities for functions of unitary operators. Some results of this paper as well as of the papers [3] and [4] were announced in [2].",

keywords = "Bernstein type inequality, Functions of operators, H{\"o}Lder-class, Operator, Perturbation, Self-adjoint operator, Unitary operators, Zygmund class",

author = "Александров, {Алексей Борисович} and Peller, {V. V.}",

year = "2010",

doi = "10.1512/iumj.2010.59.4345",

language = "English",

volume = "59",

pages = "1451--1490",

journal = "Indiana University Mathematics Journal",

issn = "0022-2518",

publisher = "Indiana University",

number = "4",

}

RIS

TY - JOUR

T1 - Functions of perturbed unbounded self-adjoint operators. Operator bernstein type inequalities

AU - Александров, Алексей Борисович

AU - Peller, V. V.

PY - 2010

Y1 - 2010

N2 - This is a continuation of our papers [3] and [4]. In those papers we obtained estimates for finite differences (δkf) (A) = f(A + K) -f(A) of the order 1 and mathematcal equation represented of the order m for certain classes of functions f , where A and K are bounded self-adjoint operators. In this paper we extend results of [3] and [4] 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 [3]. We also obtain operator Bernstein type inequalities for functions of unitary operators. Some results of this paper as well as of the papers [3] and [4] were announced in [2].

AB - This is a continuation of our papers [3] and [4]. In those papers we obtained estimates for finite differences (δkf) (A) = f(A + K) -f(A) of the order 1 and mathematcal equation represented of the order m for certain classes of functions f , where A and K are bounded self-adjoint operators. In this paper we extend results of [3] and [4] 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 [3]. We also obtain operator Bernstein type inequalities for functions of unitary operators. Some results of this paper as well as of the papers [3] and [4] were announced in [2].

KW - Bernstein type inequality

KW - Functions of operators

KW - HöLder-class

KW - Operator

KW - Perturbation

KW - Self-adjoint operator

KW - Unitary operators

KW - Zygmund class

UR - http://www.scopus.com/inward/record.url?scp=79954446139&partnerID=8YFLogxK

U2 - 10.1512/iumj.2010.59.4345

DO - 10.1512/iumj.2010.59.4345

M3 - Article

VL - 59

SP - 1451

EP - 1490

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 4

ER -

ID: 5209896