Table of contents

CONTENTS § 1. Sequences of period-doubling bifurcations § 2. Facts from the general theory of continuous one-dimensional maps § 3. The doubling transformation § 4. Properties of the Feigenbaum attractor § 5. Small random perturbations of the map g § 6. Feigenbaum universality in the multi-dimensional case and some other generalizations References

CONTENTS § 0. Introduction. Survey of results §1. A formula of Cauchy-Fantappié for differential forms in domains with piecewise smooth boundary § 2. Admissible cycles in a neighbourhood of a real manifold in and integral representations of CR-forms § 3. Construction of admissible cycles for q-concave CR-manifolds § 4. Formulae for local solutions of the tangential Cauchy-Riemann equations on q-concave CR-manifolds § 5. Holomorphic extension of CR-functions § 6. Strongly admissible cycles and integral representations of differential forms over them § 7. Theory of CR-functions and of CR-forms on q-concave CR-manifolds § 8. CR-functions and CR-forms as boundary values of holomorphic functions and of -closed forms References

CONTENTS Introduction Chapter I. (Subsidiary). Fundamental solutions of second-order parabolic equations § 1. Fundamental solutions § 2. The Cauchy problem Chapter II. Harnack's inequality § 1. Proof of Harnack's inequality § 2. Consequences of Harnack's inequality Chapter III. Two-sided estimates of classical fundamental solutions § 1. Preliminary estimates § 2. An upper estimate of the fundamental solution § 3. A lower estimate of the fundamental solution Appendix Chapter IV. Estimates of the derivatives of classical fundamental solutions of stationary equations § 1. Estimates of the time derivatives of fundamental solutions § 2. Integral estimates of special differential expressions of fundamental solutions Chapter V. Weak fundamental solutions of parabolic and elliptic equations with measurable coefficients § 1. Definitions. Energy inequalities § 2. Weak fundamental solutions of the Cauchy problem § 3. Weak fundamental solutions of stationary parabolic and elliptic equations Chapter VI. Generalizations. Applications § 1. Generalization to the case of equations containing lower-order derivatives § 2. The asymptotic proximity of solutions of the Cauchy problem. A stabilization theorem Comments References

CONTENTS § 1. Historical information § 2. Preliminary facts § 3. The concept of the complexity of ε-approximations § 4. Estimation of the complexity of ε-approximations for certain natural classes of functions § 5. The complexity of approximation of individual functions Appendix. On Marchenkov's method for investigating compositions of continuous functions References