Problems and Theorems in Analysis II

Four. Functions of One Complex Variable. Special Part.- 1. Maximum Term and Central Index, Maximum Modulus and Number of Zeros.- 2. Schlicht Mappings.- 3. Miscellaneous Problems.- Five. The Location of Zeros.- 1. Rolle's Theorem and Descartes' Rule of Signs.- 2. The Geometry of the Complex Plane and the Zeros of Polynomials.- 3. Miscellaneous Problems.- Six. Polynomials and Trigonometric Polynomials.- § 1 (1-7) Tchebychev Polynomials.- § 2 (8-15) General Problems on Trigonometric Polynomials.- § 3 (16-28) Some Special Trigonometric Polynomials.- § 4 (29-38) Some Problems on Fourier Series.- § 5 (39-43) Real Non-negative Trigonometric Polynomials.- § 6 (44-49) Real Non-negative Polynomials.- § 7 (50-61) Maximum-Minimum Problems on Trigonometric Polynomials.- § 8 (62-66) Maximum-Minimum Problems on Polynomials.- § 9 (67-76) The Lagrange Interpolation Formula.- § 10 (77-83) The Theorems of S. Bernstein and A. Markov.- § 11 (84-102) Legendre Polynomials and Related Topics.- § 12 (103-113) Further Maximum-Minimum Problems on Polynomials.- Seven. Determinants and Quadratic Forms.- § 1 (1-16) Evaluation of Determinants. Solution of Linear Equations.- § 2 (17-34) Power Series Expansion of Rational Functions.- § 3 (35-43.2) Generation of Positive Quadratic Forms.- § 4 (44-54.4) Miscellaneous Problems.- § 5 (55-72) Determinants of Systems of Functions.- Eight. Number Theory.- 1. Arithmetical Functions.- 2. Polynomials with Integral Coefficients and Integral-Valued Functions.- 3. Arithmetical Aspects of Power Series.- 4. Some Problems on Algebraic Integers.- 5. Miscellaneous Problems.- Nine. Geometric Problems.- § 1 (1-25) Some Geometric Problems.- Errata.- § 1 Additional Problems to Part One.- New Problems in EnglishEdition.- Author Index.- Topics.