Vector Valued Functions And Their Applications
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| Author | : Chuang-Gan Hu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 171 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 9401580308 |
This book is the first to be devoted to the theory of vector-valued functions with one variable. This theory is one of the fundamental tools employed in modern physics, the spectral theory of operators, approximation of analytic operators, analytic mappings between vectors, and vector-valued functions of several variables. The book contains three chapters devoted to the theory of normal functions, Hp-space, and vector-valued functions and their applications. Among the topics dealt with are the properties of complex functions in a complex plane and infinite-dimensional spaces, and the solution of vector-valued integral equations and boundary value problems by complex analysis and functional analysis, which involve methods which can be applied to problems in operations research and control theory. Much original research is included. This volume will be of interest to those whose work involves complex analysis and control theory, and can be recommended as a graduate text in these areas.
| Author | : Mauricio A. Álvarez |
| Publisher | : Foundations & Trends |
| Total Pages | : 86 |
| Release | : 2012 |
| Genre | : Computers |
| ISBN | : 9781601985583 |
This monograph reviews different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and regularization methods.
| Author | : Bernard Dacorogna |
| Publisher | : Springer |
| Total Pages | : 256 |
| Release | : 2017-05-29 |
| Genre | : Mathematics |
| ISBN | : 3319545140 |
Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.
| Author | : CK-12 Foundation |
| Publisher | : CK-12 Foundation |
| Total Pages | : 603 |
| Release | : 2010-08-15 |
| Genre | : Mathematics |
| ISBN | : 1935983016 |
CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.
| Author | : Wolfgang Arendt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 526 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 3034850751 |
Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, probability theory, mathematical physics, and other areas, and also to the development of new techniques. One important technique is given by the Laplace transform. It played an important role in the early development of semigroup theory, as can be seen in the pioneering monograph by Rille and Phillips [HP57]. But many new results and concepts have come from Laplace transform techniques in the last 15 years. In contrast to the classical theory, one particular feature of this method is that functions with values in a Banach space have to be considered. The aim of this book is to present the theory of linear evolution equations in a systematic way by using the methods of vector-valued Laplace transforms. It is simple to describe the basic idea relating these two subjects. Let A be a closed linear operator on a Banach space X. The Cauchy problern defined by A is the initial value problern (t 2 0), (CP) {u'(t) = Au(t) u(O) = x, where x E X is a given initial value. If u is an exponentially bounded, continuous function, then we may consider the Laplace transform 00 u(>. ) = 1 e-). . tu(t) dt of u for large real>. .
| Author | : Gregory Hartman |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2015 |
| Genre | : Calculus |
| ISBN | : 9781514225158 |
APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).
| Author | : V. Jeyakumar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 277 |
| Release | : 2007-10-23 |
| Genre | : Mathematics |
| ISBN | : 0387737170 |
Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems, as well as variational inequalities in finite dimensions. The treatment is motivated by a desire to expose an elementary approach to nonsmooth calculus, using a set of matrices to replace the nonexistent Jacobian matrix of a continuous vector function.
| Author | : Matthew Boelkins |
| Publisher | : Createspace Independent Publishing Platform |
| Total Pages | : 560 |
| Release | : 2018-08-13 |
| Genre | : |
| ISBN | : 9781724458322 |
Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.
| Author | : Joseph Diestel |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 338 |
| Release | : 1977-06-01 |
| Genre | : Mathematics |
| ISBN | : 0821815156 |
In this survey the authors endeavor to give a comprehensive examination of the theory of measures having values in Banach spaces. The interplay between topological and geometric properties of Banach spaces and the properties of measures having values in Banach spaces is the unifying theme. The first chapter deals with countably additive vector measures finitely additive vector measures, the Orlicz-Pettis theorem and its relatives. Chapter II concentrates on measurable vector valued functions and the Bochner integral. Chapter III begins the study of the interplay among the Radon-Nikodym theorem for vector measures, operators on $L_1$ and topological properties of Banach spaces. A variety of applications is given in the next chapter. Chapter V deals with martingales of Bochner integrable functions and their relation to dentable subsets of Banach spaces. Chapter VI is devoted to a measure-theoretic study of weakly compact absolutely summing and nuclear operators on spaces of continuous functions. In Chapter VII a detailed study of the geometry of Banach spaces with the Radon-Nikodym property is given. The next chapter deals with the use of Radon-Nikodym theorems in the study of tensor products of Banach spaces. The last chapter concludes the survey with a discussion of the Liapounoff convexity theorem and other geometric properties of the range of a vector measure. Accompanying each chapter is an extensive survey of the literature and open problems.
| Author | : Don H. Tucker |
| Publisher | : |
| Total Pages | : 488 |
| Release | : 1973 |
| Genre | : Mathematics |
| ISBN | : |
