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1
Content available Hilbert-Schmidtness of weighted composition operators and their differences on Hardy spaces
Lo Ching-on, Loh Anthony Wai-keung
Opuscula Mathematica
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2020
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Vol. 40, no. 4
495--507
EN
Let u and φ be two analytic functions on the unit disk D such that φ (D) ⊂ D. A weighted composition operator uCφ induced by u and φ is defined on H2, the Hardy space of D, by [formula] for every ∫ in H2. We obtain sufficient conditions for Hilbert-Schmidtness of v,Cv on H2 in terms of function-theoretic properties of u and φ. Moreover, we characterize Hilbert-Schmidt difference of two weighted composition operators on H2.
2
Compactness result and its applications in integral equations
Krukowski M., Przeradzki B.
Journal of Applied Analysis
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2016
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Vol. 22, nr 2
153--161
EN
A version of the Arzelà–Ascoli theorem for X being a σ-locally compact Hausdorff space is proved. The result is used in proving compactness of Fredholm, Hammerstein and Urysohn operators. Two fixed point theorems, for Hammerstein and Urysohn operators, are derived on the basis of Schauder fixed point theorem.
3
Content available remote Series representation of compact linear operators in Banach spaces
Edmunds D., Lang J.
Commentationes Mathematicae
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2016
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Vol 56, No. 1
17--27
EN
Let p∈(1,∞) and I=(0,1); suppose that T:Lp(I)→Lp(I) is a~compact linear map with trivial kernel and range dense in Lp(I). It is shown that if the Gelfand numbers of T decay sufficiently quickly, then the action of T is given by a series with calculable coefficients. The special properties of Lp(I) enable this to be established under weaker conditions on the Gelfand numbers than in earlier work set in the context of more general spaces.
4
Content available Inequalities for regularized determinants of operators with the Nakano type modulars
Gil M.
Opuscula Mathematica
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2013
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Vol. 33, no. 2
283--291
EN
Let {pk} be a nondecreasing sequence of integers, and A be a compact operator in a Hilbert space whose eigenvalues and singular values are Λk(A) and Sk(A) (k=1,2,...) respectively. We establish upper and lower bounds for the regularized determinant [formula] for a constant c ∈ (O,1).
5
Content available Hyponormal differential operators with discrete spectrum
Ismailov Z. I., Unluyol E.
Opuscula Mathematica
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2010
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Vol. 30, no. 1
79-94
EN
In this work, we first describe all the maximal hyponormal extensions of a minimal operator generated by a linear differential-operator expression of the first-order in the Hilbert space of vector-functions in a finite interval. Next, we investigate the discreteness of the spectrum and the asymptotical behavior of the modules of the eigenvalues for these maximal hyponormal extensions.
6
Content available remote Bochner representable operators on Köthe-Bochner spaces
Nowak M.
Commentationes Mathematicae
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2008
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Vol. 48, [Z] 2
113-119
EN
Let E be a Banach function space and X be a real Banach space. We study Bochner representable operators from a K¨othe-Bochner space E(X) to a Banach space Y . We consider the problem of compactness and weak compactness of Bochner representable operators from E(X) (provided with the natural mixed topology) to Y .
7
Content available remote The embeddability of C0 in spaces of operators
Ghenciu I., Lewis P.
Bulletin of the Polish Academy of Sciences. Mathematics
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2008
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Vol. 56, no 3-4
239-256
EN
Results of Emmanuele and Drewnowski are used to study the containment of c0 in the space Kw* (X*, Y), as well as the complementation of the space Kw* (X*,Y) of w*-w compact operators in the space Lw*(X*, Y) of w*-w operators from X* to Y.
8
Content available remote Weighted composition operators via Berezin transform and Carleson measure
Kumar R., Singh K. J.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2006
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Vol. 46, [Z] 1
63-78
EN
In this paper, we study the boundedness and the compactness of weighted composition operators on Hardy spaces and weighted Bergman spaces of the unit polydisc in C^n.
9
Content available remote Complemented spaces of operators
Bator E. M., Lewis P. W.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2002
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Vol. 50, no 4
413-416
EN
The complementation of various classes of operators in the space L(E, F) of bounded linear operators between Banach spaces E and F is studied.
10
A second kind integral equation formulation for the interaction between a solid particle and a compound drop at low Reynolds number
Kohr M.
Applied Mechanics and Engineering
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2000
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Vol. 5, no 3
557-577
EN
In this paper, we determine a boundary integral formulation for the motion and deformation of a compound drop due to its interaction with a solid particle. The problem is reduced to a system of Fredholm integral equations of the second kind. We prove that this system has a unique continous solution when the boundaries of the flow are Lyapunov surfaces and the boundary data are continous.
11
An integral method for two-dimensional stokes flows past rigid obstacles in the half-plane
Kohr M.
Applied Mechanics and Engineering
|
1998
|
Vol. 3, no 1
5-24
EN
The problem of determining the slow viscous flow of a fluid past a cylinder with an arbitrary cross section, in a domain with boundary limited by a plane wall, is formulated as a system of Fredholm linear integral equations of the second kind. We next complete the double-layer potentials of the system with some terms having singularities located inside the obstacle and which satisfy the nonslip boundary condition on the wall. We next prove that this system of integral equations has a unique continuous solution when the boundary of the particle is a Lyapunov curve. Also, the numerical results are given for the case of a fixed circular obstacle. For the numerical solution we use a standard boundary element technique.
12
An direct boundary integral equations method to Stokes flow past rigid bodies in ground effect
Kohr M.
Applied Mechanics and Engineering
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1998
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Vol. 3, no 2
217-232
EN
The aim of this paper is to give a direct boundary integral equations method for the slow motion of some rigid bodies of an arbitrary shape, near a plane wall in a viscous incompressible fluid. By using an integral representation of the velocity field as a sum between single-layer potentials and double-layer potentials, the problem is reduced to the study of a Fredholm integral system of the second kind. By following the properties of the single-layer and double-layer operators, the existence and uniqueness result of the corresponding solution is given. The numerical results are obtained by a standard boundary element method.
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