By Ahmad Al-Salman, Hussain Al-Qassem (auth.), Stefan Samko, Amarino Lebre, António F. dos Santos (eds.)
These complaints include a wide a part of the papers offered on the In ternational convention Factorization, Singular Operators and similar difficulties, which used to be held from January 28 to February 1, 2002, on the collage of th Madeira, Funchal, Portugal, to mark Professor Georgii Litvinchuk's 70 beginning day. specialists in numerous fields got here to this convention to pay tribute to the nice achievements of Professor Georgii Litvinchuk within the improvement of vari ous parts of operator thought. the most topics of the convention have been focussed round the concept of singular kind operators and factorization difficulties, yet different themes similar to capability concept and fractional calculus, to call yet a pair, have been additionally awarded. The aim of the convention used to be to collect mathematicians from var ious fields inside operator idea and serve as idea with a purpose to spotlight contemporary advances in difficulties lots of which have been initially studied by means of Profes sor Litvinchuk and his medical institution. A moment objective used to be to stimulate in ternational collaboration even additional and advertise the interplay of alternative ways in present examine in those parts. The court cases may be of significant curiosity to researchers in Operator The ory, actual and complicated research, sensible and Harmonic research, strength conception, Fractional Calculus and different parts, in addition to to graduate scholars searching for the newest results.
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Additional info for Factorization, Singular Operators and Related Problems: Proceedings of the Conference in Honour of Professor Georgii Litvinchuk
Example text
2] Antonevich, A. , The essential spectra of a weighted shift operator in the spaces of continuous and differentiable functions. In: Spectral and evolutionary problems, Vo!. 8 (Sevastopol, 1997), 3~ 12. , Simferopol', 1998. , Functional Differential Equations: 2. C* -applications. Parts 1, 2, Pitman Monographs and Surveys in Pure and Applied Mathematics 94, 95. Longman, Harlow, 1998. [4] Antonevich, A. , Functional Differential Equations: I. C· -theory, Pitman Monographs and Surveys in Pure and Applied Mathematics, 70.
1 with L = f~l, we deduce that 1+ E Fl'~. 1 and the equality Pb = P(J- . ;l) imply that Pb E Fl'~. Let Pn be the orthogonal projection of l'2(Z+) onto l'2({O, ... ,n -1}) and put Qn = I -Pn . The Hankel operators H(g) and H(g) generated by a function 9 E Loo are given by the matrices 47 SLOWLY GROWING PSEUDOSPECTRA We denote b- I = f+J~1 by c. In [5J (also see [2J or [6, pp. 2) j=O where K = H(b)H(c). e;, we have 2 IIQnH(b)112 ::; ~ 00 (n + k)2a n 2a - 1 Ibn+kl 2 = 0 (1) n 2a - 1 . 2) converges for all sufficiently large n.
6] Kravchenko, V. G. and Litvinchuk, G. , Introduction to the Theory of Singular Integral Operators with Shift, Mathematics and its Applications, 289. Kluwer Academic Publishers, Dordrecht, 1994. , Differentiable dynamics. An introduction to the orbit structure of diffeomorphisms. T. -London, 1971. pt This paper is dedicated to Prof. G. S. L2(z)8zw = A(z)w + B(z)w + F(z), where w(z, z) = u + iv is an unknown complex-valued function, and the related integral operators and boundary value problems.