Ha-Plitz Operators: A Survey of Some Recent Results

作者: N. K. Nikol’skii

DOI: 10.1007/978-94-009-5374-1_5

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摘要: Originally, Hankel and Toeplitz operators are defined as acting on l2 having matrices with entries depending only the sum or, respectively, difference of indices: \( \Gamma = {\left\{ {{\gamma_{n + k}}} \right\}_{n,k \geqslant 0}} \), T \left\{ {{t_{n - \right\}{}_{n,k 0} \). Many close relations such (matrices) to various problems algebra, analysis, differential equations were discovered early in last century. But spectral theories start their development late 50th. Now they joined within theory operators.

参考文章(18)
Н. К. Никольский, Лекции об операторе сдвига Наука. ,(1980)
R. Douglas, Banach algebra techniques in the theory of Toeplitz operators American Mathematical Society. ,vol. 15, ,(1973) , 10.1090/CBMS/015
Donald Sarason, Weak-star generators of $H^{\infty}$. Pacific Journal of Mathematics. ,vol. 17, pp. 519- 528 ,(1966) , 10.2140/PJM.1966.17.519
Donald Sarason, Function theory on the unit circle Virginia Polytechnic Institute and State University. ,(1978)
Donald Sarason, Generalized interpolation in Transactions of the American Mathematical Society. ,vol. 127, pp. 179- 203 ,(1967) , 10.1090/S0002-9947-1967-0208383-8
N. K. Nikol'skil, V. I. Vasjunin, Control subspaces of minimal dimension and root vectors Integral Equations and Operator Theory. ,vol. 6, pp. 274- 311 ,(1983) , 10.1007/BF01691899
Thomas H. Wolff, Two algebras of bounded functions Duke Mathematical Journal. ,vol. 49, pp. 321- 328 ,(1982) , 10.1215/S0012-7094-82-04920-1
Douglas N. Clark, ON THE POINT SPECTRUM OF A TOEPLITZ OPERATOR Transactions of the American Mathematical Society. ,vol. 126, pp. 251- 266 ,(1967) , 10.1090/S0002-9947-1967-0201968-4
Ky Fan, A generalization of Tychonoff's fixed point theorem Mathematische Annalen. ,vol. 142, pp. 305- 310 ,(1961) , 10.1007/BF01353421