Complex Analysis, Operators, and Related Topics: The S. A. by Victor P. Havin, Nikolai K. Nikolski

By Victor P. Havin, Nikolai K. Nikolski

This quantity is dedicated to a few topical difficulties and diverse functions of operator idea and its interaction with glossy advanced research. It includes 30 rigorously chosen surveys and study papers.

The major topics of the quantity include:
· loose interpolation by means of analytic services in its improvement from the pathbreaking works by way of L. Carleson as much as the latest achievements and in its connections with the idea of singular quintessential operators and Carleson-type embedding theorems, second difficulties etc.
· Szökefalvi-Nagy-Foias version areas studied from the viewpoint of holomorphic spaces
· holomorphic areas (Hardy, Bergman, Hölder, and Sobolev spaces)
· analytic services delicate as much as the boundary with their refined houses on the topic of the Nevanlinna-Smirnov factorization, department and multiplication, and nil sets
· a brand new method of weighted inequalities for singular integrals in line with the Bellman functionality in optimization theory;
· the uncertainty precept in harmonic research and, specifically, a whole model of Turan‘s lemma on trigonometric sums
· Hankel operators and desk bound Gaussian processes
· Fourier multipliers, and spectral research of a few differential operators.

These topics are united via the "operator theoretic ideology" and systematic use of recent functionality theoretical techniques.
The ebook is devoted to the reminiscence of S. A. Vinogradov. It includes a bibliographical be aware (with a full of life portrait) of S. A. Vinogradov, a close survey of his mathematical achievements, and an entire checklist of courses, in addition to the translations of 2 of Vinogradov‘s surveys whose Russian originals at the moment are rarely accessible.

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Additional resources for Complex Analysis, Operators, and Related Topics: The S. A. Vinogradov Memorial Volume

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Let lrv be the space of all sequences x = {Xk}~o of complex numbers with finite norm l1 00 denote by VA the space of all functions ! f regular in ]j)) and such that 11" sup O. ~ 1. It is known that VA eli [Hol. Theorem 1. Let {~k}~o be a sequence in]j)) satisfying the following conditions: ~k # ~m if k # m, and 11- ~k+11 ::; 11- ~kl, k = 0,1, .... If {~k}~=O c B A, then the following are equivalent: 1. 8 1(l1) = bv; 2. 81 (VA) = bv; 3. {~k}~O satisfies (*); 8 1 denotes the operator defined by 81 (f) = {j(~k)}~=o, f Eli.

Sem. -Petersburg. Otde!. Mat. Inst. Steklov. (POMI), 206 (1993),40-54,174 (Russian); English trans!. in J. Math. , 80 (1996), no. 4. [40] S. A. Vinogradov, Multiplicative properties of some £P -spaces of analytic junctions, Summaries of reports of the All-Russian seminar "Function theory". Syktyvkar CU, 1993, pp. 10-11 (Russian). [41] S. A. , 1574 (1994), Part II, 283-285. [42] S. A. Vinogradov, Multiplication and division in the space of analytic functions with an area-integrable derivative, and in some related spaces, Zap.

Eidelheit and B. M. Makarov applicable to a large class of "freely solvable" moment problems in linear topological spaces. Historically, this is probably the first example of a phenomenon which is the theme of our thesis, namely, the phenomenon of free interpolation by analytic functions. The rigid interconnection of values of an analytic functions is destroyed on a "sparse" A C G; functions of class A( G) conceal their analyticity when considered on A only, any function defined on A being the trace of an element of A( G).

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