Author: Boris I_Akovlevich LevinPublisher: American Mathematical Soc.
ISBN: 0821845055
Category : Mathematics
Languages : en
Pages : 542
Book Description
Distribution of Zeros of Entire Functions
Author: Boris I_Akovlevich LevinPublisher: American Mathematical Soc.
ISBN: 0821845055
Category : Mathematics
Languages : en
Pages : 542
Book Description
Distribution of Zeros of Entire Functions
Author: B. Ja LevinIntroduction to the Theory of Entire Functions of Several Variables
Author: Lev Isaakovich RonkinPublisher: American Mathematical Soc.
ISBN: 9780821886687
Category : Mathematics
Languages : en
Pages : 286
Book Description
Zeros of Gaussian Analytic Functions and Determinantal Point Processes
Author: John Ben HoughPublisher: American Mathematical Soc.
ISBN: 0821843737
Category : Mathematics
Languages : en
Pages : 170
Book Description
Examines in some depth two important classes of point processes, determinantal processes and 'Gaussian zeros', i.e., zeros of random analytic functions with Gaussian coefficients. This title presents a primer on modern techniques on the interface of probability and analysis.
Random Polynomials
Author: A. T. Bharucha-ReidPublisher: Academic Press
ISBN: 148319146X
Category : Mathematics
Languages : en
Pages : 223
Book Description
Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Random Polynomials focuses on a comprehensive treatment of random algebraic, orthogonal, and trigonometric polynomials. The publication first offers information on the basic definitions and properties of random algebraic polynomials and random matrices. Discussions focus on Newton's formula for random algebraic polynomials, random characteristic polynomials, measurability of the zeros of a random algebraic polynomial, and random power series and random algebraic polynomials. The text then elaborates on the number and expected number of real zeros of random algebraic polynomials; number and expected number of real zeros of other random polynomials; and variance of the number of real zeros of random algebraic polynomials. Topics include the expected number of real zeros of random orthogonal polynomials and the number and expected number of real zeros of trigonometric polynomials. The book takes a look at convergence and limit theorems for random polynomials and distribution of the zeros of random algebraic polynomials, including limit theorems for random algebraic polynomials and random companion matrices and distribution of the zeros of random algebraic polynomials. The publication is a dependable reference for probabilists, statisticians, physicists, engineers, and economists.
Entire Functions
Author: Publisher: Academic Press
ISBN: 0080873138
Category : Mathematics
Languages : en
Pages : 289
Book Description
Entire Functions
Lectures on Entire Functions
Author: B. Ya LevinPublisher: American Mathematical Soc.
ISBN: 0821808974
Category : Mathematics
Languages : en
Pages : 266
Book Description
As a brilliant university lecturer, B. Ya. Levin attracted a large audience of working mathematicians and of students from various levels and backgrounds. For approximately 40 years, his Kharkov University seminar was a school for mathematicians working in analysis and a center for active research. This monograph aims to expose the main facts of the theory of entire functions and to give their applications in real and functional analysis. The general theory starts with the fundamental results on the growth of entire functions of finite order, their factorization according to the Hadamard theorem, properties of indicator and theorems of Phragmen-Lindelof type.
Entire and Meromorphic Functions
Author: Lee A. RubelPublisher: Springer Science & Business Media
ISBN: 1461207355
Category : Mathematics
Languages : en
Pages : 196
Book Description
Mathematics is a beautiful subject, and entire functions is its most beautiful branch. Every aspect of mathematics enters into it, from analysis, algebra, and geometry all the way to differential equations and logic. For example, my favorite theorem in all of mathematics is a theorem of R. NevanJinna that two functions, meromorphic in the whole complex plane, that share five values must be identical. For real functions, there is nothing that even remotely corresponds to this. This book is an introduction to the theory of entire and meromorphic functions, with a heavy emphasis on Nevanlinna theory, otherwise known as value-distribution theory. Things included here that occur in no other book (that we are aware of) are the Fourier series method for entire and mero morphic functions, a study of integer valued entire functions, the Malliavin Rubel extension of Carlson's Theorem (the "sampling theorem"), and the first-order theory of the ring of all entire functions, and a final chapter on Tarski's "High School Algebra Problem," a topic from mathematical logic that connects with entire functions. This book grew out of a set of classroom notes for a course given at the University of Illinois in 1963, but they have been much changed, corrected, expanded, and updated, partially for a similar course at the same place in 1993. My thanks to the many students who prepared notes and have given corrections and comments.
Fewnomials
Author: A. G. KhovanskiĭPublisher: American Mathematical Soc.
ISBN: 9780821898307
Category : Mathematics
Languages : en
Pages : 154
Book Description
The ideology of the theory of fewnomials is the following: real varieties defined by "simple", not cumbersome, systems of equations should have a "simple" topology. One of the results of the theory is a real transcendental analogue of the Bezout theorem: for a large class of systems of *k transcendental equations in *k real variables, the number of roots is finite and can be explicitly estimated from above via the "complexity" of the system. A more general result is the construction of a category of real transcendental manifolds that resemble algebraic varieties in their properties. These results give new information on level sets of elementary functions and even on algebraic equations. The topology of geometric objects given via algebraic equations (real-algebraic curves, surfaces, singularities, etc.) quickly becomes more complicated as the degree of the equations increases. It turns out that the complexity of the topology depends not on the degree of the equations but only on the number of monomials appearing in them. This book provides a number of theorems estimating the complexity of the topology of geometric objects via the cumbersomeness of the defining equations. In addition, the author presents a version of the theory of fewnomials based on the model of a dynamical system in the plane. Pfaff equations and Pfaff manifolds are also studied.
Entire Functions and Related Parts of Analysis
Author: Jacob KorevaarPublisher: American Mathematical Soc.
ISBN: 0821814117
Category : Mathematics
Languages : en
Pages : 562
Book Description