A Note on Fractional Powers of Strongly Positive Operators and Their Applications

Let A be a closed operator on a separable Hilbert space with the spectrum in the open right half-plane and a bounded Hermitian component, and let the resolvent of A be a Hilbert-Schmidt operator. The paper deals with the function h µ (A) = ∞ 0 (A + tI) −1 dµ(t),where µ is a nondecreasing function and I is the unit operator. We establish norm estimates and perturbations results for h µ (A). As particular cases the fractional powers and logarithm of A are considered.

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“…For the classical results, see [8,9]. The recent investigations can be found in [1,2,4,5], [10]- [15] and the references given therein.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Equivalence of Weighted Dt-Moduli of Convex Functions

Al-Muhja¹,

Akhadkulov²,

Ahmad³

2021

Int. J. of Appl. Math.

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“…For the classical results, see [8,9]. The recent investigations can be found in [1,2,4,5], [10]- [15] and the references given therein.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Estimates for Fractional Powers and Logarithm of Operators With Hilbert-Schmidt Resolvents and Perturbation Results

Gil'

2021

Int. J. of Appl. Math.

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“…Such conditions usually are identified as nonlocal boundary conditions and reflect situations when the data on the domain boundary cannot be measured directly, or when the data on the boundary depend on the data inside the domain. The well-posedness of various nonlocal boundary value problems for partial differential and difference equations has been studied extensively by many researchers (see, e.g., [5][6][7][8][9][10][11][12][13][14][15][16][17][22][23][24] and the references given therein).…”

Section: Introductionmentioning

confidence: 99%

Well-posedness of a nonlocal boundary value difference elliptic problem

Ashyralyev

Hamad

2019

Math. Model. Nat. Phenom.

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The second order of approximation two-step difference scheme for the numerical solution of a nonlocal boundary value problem for the elliptic differential equation [see formula in PDF] in an arbitrary Banach space E with the positive operator A is presented. The well-posedness of the difference scheme in Banach spaces is established. In applications, the stability, almost coercive stability and coercive stability estimates in maximum norm in one variable for the solutions of difference schemes for numerical solution of two type elliptic problems are obtained.

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A Note on Fractional Powers of Strongly Positive Operators and Their Applications

Abstract: The present paper deals with fractional powers of positive operators in a Banach space. The main theorem concerns the structure of fractional powers of positive operators in fractional spaces. As applications, the structure of fractional powers of elliptic operators is studied.

Cited by 7 publications

References 23 publications

Equivalence of Weighted Dt-Moduli of Convex Functions

Equivalence of Weighted Dt-Moduli of Convex Functions

Estimates for Fractional Powers and Logarithm of Operators With Hilbert-Schmidt Resolvents and Perturbation Results

Well-posedness of a nonlocal boundary value difference elliptic problem

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