scholarly journals On properties of multiplication conditional type operators between Lp-space

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1933-1940
Author(s):  
Yousef Estaremi
Keyword(s):  
Measure Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Closed Range ◽  
Lp Space ◽  
Lp Spaces ◽  
Necessary And Sufficient

In this paper, firstwe give some necessary and sufficient conditions for multiplication conditional type operators between two Lp-spaces to have closed range. Then we investigate Fredholm ones when the underlying measure space is non-atomic. Finally we give some examples.

scholarly journals On an interpolation process of Lagrange-Hermite type

2012 ◽  
Vol 91 (105) ◽  
pp. 163-175
Author(s):  
Giuseppe Mastroianni ◽  
Gradimir Milovanovic ◽  
Incoronata Notarangelo
Keyword(s):  
Hermite Polynomial ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Necessary And Sufficient Conditions ◽  
Interpolation Process ◽  
Lp Spaces ◽  
Related Operator ◽  
Optimal Estimates ◽  
Necessary And Sufficient

We consider a Lagrange-Hermite polynomial, interpolating a function at the Jacobi zeros and, with its first (r?1) derivatives, at the points ?1. We give necessary and sufficient conditions on the weights for the uniform boundedness of the related operator in certain suitable weighted Lp-spaces, 1 < p < 1, proving a Marcinkiewicz inequality involving the derivative of the polynomial at ?1. Moreover, we give optimal estimates for the error of this process also in the weighted uniform metric.

scholarly journals Basic properties of finite sum of weighted composition operators

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 4005-4019
Author(s):  
Abolghasem Alishahi ◽  
Saeedeh Shamsigamchi ◽  
Ali Ebadian
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Lp Spaces ◽  
Basic Properties ◽  
Weighted Composition ◽  
Finite Sums ◽  
Finite Sum ◽  
Necessary And Sufficient

In this paper,we continue the study of finite sum of weighted composition operators between different Lp-spaces that was investigated by Jabbarzadeh and Estaremi in 2012. Indeed, we first obtain some necessary and sufficient conditions for boundedness of the finite sums of weighted composition operators between distinct Lp-spaces. In the sequel, we investigate the compactness of finite sum of weighted composition operators. By using theorems of boundedness and compactness, we estimate the essential norms of these operators. Finally, some examples to illustrate the main results are given.

scholarly journals Interchanging a limit and an integral: necessary and sufficient conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Takashi Kamihigashi
Keyword(s):  
Measure Space ◽  
Sufficient Conditions ◽  
Finite Measure ◽  
Necessary And Sufficient Conditions ◽  
Integrable Functions ◽  
Finite Measure Space ◽  
Pointwise Limit ◽  
Necessary And Sufficient

AbstractLet $\{f_{n}\}_{n \in \mathbb {N}}$ { f n } n ∈ N be a sequence of integrable functions on a σ-finite measure space $(\Omega, \mathscr {F}, \mu )$ ( Ω , F , μ ) . Suppose that the pointwise limit $\lim_{n \uparrow \infty } f_{n}$ lim n ↑ ∞ f n exists μ-a.e. and is integrable. In this setting we provide necessary and sufficient conditions for the following equality to hold: $$ \lim_{n \uparrow \infty } \int f_{n} \, d\mu = \int \lim_{n \uparrow \infty } f_{n} \, d\mu. $$ lim n ↑ ∞ ∫ f n d μ = ∫ lim n ↑ ∞ f n d μ .

A general version of Neubauer’s lemma and closed range almost closed operators

2019 ◽  
Vol 13 (07) ◽  
pp. 2050124
Author(s):  
Abdellah Gherbi ◽  
Sanaa Messirdi ◽  
Bekkai Messirdi
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Closed Operator ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
General Version ◽  
Closed Range ◽  
Closed Operators ◽  
Necessary And Sufficient ◽  
Closed Linear Operators

In this paper, almost closed subspaces and almost closed linear operators are described in a Hilbert space. We show Neubauer’s lemma and we give necessary and sufficient conditions for an almost closed operator to be with closed range and we exhibit sufficient conditions under which it is either closed or closable.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Nonlinear boundary-value problems for degenerate differential-algebraic systems

2020 ◽  
Vol 17 (3) ◽  
pp. 313-324
Author(s):  
Sergii Chuiko ◽  
Ol'ga Nesmelova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Algebraic System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Nonlinear ◽  
Differential Algebraic System ◽  
Linear Differential ◽  
Necessary And Sufficient

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

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