Complex Analysis and Dynamical Systems VII.

Cover -- Title page -- Contents -- Preface -- Conference Program -- Accuracy of reconstruction of spike-trains with two near-colliding nodes -- 1. Introduction -- 2. Setting of the problem -- 3. Visualization of the error sets _{ }( ) -- 4. Prony curves and error amplification: main results -- 5. Proofs -- 6. A case of complex nodes -- Acknowledgements -- References -- Exact solutions to a Muskat problem with line distributions of sinks and sources -- 1. Introduction -- 2. The Schwarz function method of finding exact solutions for the Muskat problem -- 3. A two-phase mother body -- 4. Examples of specific Γ(0) -- 5. Conclusions -- Acknowledgments -- References -- Modulus of families of walks on graphs -- 1. Introduction -- 2. Notations and Definitions -- 3. Definition of modulus of families of walks -- 4. Beurling's criterion for extremality -- 5. General properties for modulus of walk families -- 6. Capacity -- 7. Essential subfamilies and inequality conditions for admissibility -- 8. Modulus as a Convex Program and the Karush-Kuhn-Tucker conditions -- 9. An algorithm for approximating the modulus -- 10. Conclusion -- Acknowledgement -- References -- Uniqueness of contact Hamiltonians of topological strictly contact isotopies -- 1. Introduction -- 2. Review of contact geometry -- 3. Topological strictly contact isotopies -- 4. The proof of Theorem 1.1 -- References -- A Triple Principle (for Curves, Surfaces and Complex Functions) and the Universal Version of Value Distribution Theory -- Introduction -- 1. The winding principles for the plane curves -- 2. A counterpart of the principle for the surfaces -- 3. A counterpart of the principle for the complex functions -- 4. Universal version of value distribution for functions in a given domain -- References -- Characterization of orthogonal polynomials- A new proof of Bochner's theorem.

1. Introduction -- 2. Classification theorem -- 3. Orthogonal polynomials with orthogonal derivatives -- 4. Conclusions -- References -- Decomposition of the Kostlan-Shub-Smale model for random polynomials -- 1. Introduction -- 2. The coefficients corresponding to invariant Euclidean structures -- 3. The coefficients for the space of homogeneous polynomials -- 4. The scaling limit of the coefficients ⱼ as →∞ -- 5. Approximation by polynomials of lower degree -- References -- Differentiability of ring homeomorphisms with controlled -module -- 1. Introduction -- 2. Auxiliary results -- 3. Proof of Theorem 1.1 -- 4. Differentiability condition for integrable majorant -- References -- Some inequalities for holomorphic self-maps of the unit disc with two fixed points -- 1. Introduction -- 2. Proof of Theorem 1 -- 3. Proof of Theorem 2 -- References -- Interpolation and Cubature at Geronimus Nodes Generated by Different Geronimus Polynomials -- 1. Introduction -- 2. Geronimus polynomials -- 3. Interpolation nodes -- 4. Construction of Lagrange polynomials -- 5. Proof of Propositions 2 and 3 -- 6. Further comments -- References -- Characterizations to the fractional Sobolev inequality -- 1. Introduction -- 2. Notation and preliminaries -- 3. The main result -- 4. On the fractional capacity and perimeter -- References -- Elliptic perturbations of dynamical systems with a proper node -- 1. Introduction -- 2. The case of homogeneous differential equation -- 3. The case of homogeneous boundary condition -- 4. The case of right-hand side of zero average value -- 5. Conclusion -- 6. Appendix -- References -- Krull dimensions of rings of holomorphic functions -- 1. Hyperreal numbers -- 2. Krull dimension of ample rings -- 3. Ampleness of rings of holomorphic functions -- References -- Complex geodesics and variational calculus for univalent functions.

1. Key theorems on invariant metrics and geodesics on \Te spaces -- 2. Proof of Theorem 1.1 -- 3. Applications to geometric complex analysis -- 4. New phenomena -- References -- Analytic reflection across analytic Jordan curves -- 1. Introduction -- 2. A measure for the analyticity of a Jordan curve -- 3. Extendibility condition for ℭ -- 4. Influence of an affine transformation -- 5. Another proof of Theorem 2 -- References -- Compositions of polyharmonic mappings -- 1. Introduction and Main Results -- 2. Some Notations and Preliminary Results -- 3. The Proofs of the Main Theorems -- References -- On Marcinkiewicz-Zygmund inequalities at Jacobi zeros and their Bessel function cousins -- 1. Introduction -- 2. Proofs of Theorem 1.1 and Corollary 1.2 -- 3. Proofs of Theorem 1.3 and Corollary 1.4 -- References -- Nonminimal cyclic invariant subspaces of hyperbolic composition operators -- 1. Introduction -- 2. Inner functions -- 3. Non-inner functions -- References -- An improved defect relation for holomorphic curves in projective varieties -- 1. Statement of the Main Results -- 2. Proof of the Main Theorem -- References -- A porosity theorem for a class of nonexpansive set-valued mappings -- 1. Introduction and preliminaries -- 2. Main result -- 3. Auxiliary results -- 4. Proof of Theorem 2.1 -- References -- The Khavinson-Shapiro conjecture for domains with a boundary consisting of algebraic hypersurfaces -- 1. Introduction -- 2. Surjectivity of Fischer operators. -- 3. On the conjecture (CS) -- References -- Shadow Problem for the Tangent Bundle of Straight Lines on a Sphere -- References -- Back Cover.

This volume contains the proceedings of the Seventh International Conference on Complex Analysis and Dynamical Systems, held from May 10-15, 2015, in Nahariya, Israel. The papers in this volume range over a wide variety of topics in the interaction between various branches of mathematical analysis. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, geometry, harmonic analysis, and partial differential equations, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.