Linear and complex analysis problem book 3, Part II / V. P. Havin, N. K. Nikolski

This problem book 3, consisting of two volumes with 500 pages each, is the third edition of the Linear and Complex Analysis problem book. The first edition started in 1978 with 99 research problems concerning analytic functions, linear function spaces and linear operators, the second edition from 1984 contained 199 problems, and the present edition offers 341 problems. The increase results mainly from many new problems in operator- and function Theory. The problems are grouped into 20 chapters, which are provided with introductions. These intend to help the reader to grasp the general direction of the chapter, to record additional bibliography and to make historical comments. The chapter headings are the following.

Volume 1: 1. Banach spaces, 2. Banach algebras, 3. Probabilistic problems, 4. Holomorphic operator functions, 5. General operator theory. 6. Perturbation- and scattering theory, 7. Hankel and Toeplitz operators, 8. Operators close to normals, 9. Functional model, 10. Singular integrals.

Volume 2: 11. Spectral analysis and synthesis, 12. Approximations and capacities, 13 Orthogonal polynomials, 14. Uniqueness, moments and normality, 15. Interpolation bases and multipliers, 16. Entire and subharmonic functions, 17. Cn , 18. Geometric function theory, 19. Holomorphic dynamics, 20. Miscellaneous problems.

Both volumes are provided with a subject index and an author index. We recommend this book for every mathematician working in analysis. (Zentralblatt)