Elementary Functional Analysis (93 results)

paperback. Condition: Good.

Paperback. Condition: Good. In this introductory work on mathematical analysis, the noted mathematician Georgi E. Shilov begins with an extensive and important chapter on the basic structures of mathematical analysis: linear spaces, metric spaces, normed linear spaces, Hilbert spaces, and normed algebras. The standard models for all these spaces are sets of functions (hence the term functional analysis), rather than sets of points in a finite-dimensional space.Chapter 2 is devoted to differential equations, and contains the basic theorems on existence and uniqueness of solutions of ordinary differential equations for functions taking values in a Banach space. The solution of the linear equation with constant (operator) coefficients is written in general form in terms of the exponential of the operator. This leads, in the finite-dimensional case, to explicit formulas not only for the solutions of first-order equations, but also to the solutions of higher-order equations and systems of equations. The third chapter presents a theory of curvature for curve in a multidimensional space.The final two chapters essentially comprise an introduction to Fourier analysis. In the treatment of orthogonal expansions, a key role is played by Fourier series and the various kinds of convergence and summability for such series. The material on Fourier transforms, in addition to presenting the more familiar theory, also deals with problems in the complex domain, in particular with problems involving the Laplace transform.Designed for students at the upper-undergraduate or graduate level, the text includes a set of problems for each chapter, with hints and answers at the end of the book.…

Paperback. Condition: Good. In this introductory work on mathematical analysis, the noted mathematician Georgi E. Shilov begins with an extensive and important chapter on the basic structures of mathematical analysis: linear spaces, metric spaces, normed linear spaces, Hilbert spaces, and normed algebras. The standard models for all these spaces are sets of functions (hence the term functional analysis), rather than sets of points in a finite-dimensional space.Chapter 2 is devoted to differential equations, and contains the basic theorems on existence and uniqueness of solutions of ordinary differential equations for functions taking values in a Banach space. The solution of the linear equation with constant (operator) coefficients is written in general form in terms of the exponential of the operator. This leads, in the finite-dimensional case, to explicit formulas not only for the solutions of first-order equations, but also to the solutions of higher-order equations and systems of equations. The third chapter presents a theory of curvature for curve in a multidimensional space.The final two chapters essentially comprise an introduction to Fourier analysis. In the treatment of orthogonal expansions, a key role is played by Fourier series and the various kinds of convergence and summability for such series. The material on Fourier transforms, in addition to presenting the more familiar theory, also deals with problems in the complex domain, in particular with problems involving the Laplace transform.Designed for students at the upper-undergraduate or graduate level, the text includes a set of problems for each chapter, with hints and answers at the end of the book.…

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paperback. Condition: Near Fine. Condition Notes: Excellent, unmarked copy with little wear and tight binding. We ship in recyclable American-made mailers. 100% money-back guarantee on all orders.

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hardcover. Condition: Very Good. Hardcover. No dust jacket. Red cloth boards with silver lettering on the spine. Some discoloration on edges front shelf wear. Previous owners name on front free endpaper. Overall very good condition, pages are crisp, binding is strong. No date on the title page. Copyright page dated 1974. 334 pages. We are a real brick and mortar bookstore and ship books everyday. This listing was written by an actual person with the book in front of them for inspection. Please email with questions or to request photographs. …

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paperback. Condition: Near Fine. Condition Notes: Excellent, unmarked copy with little wear and tight binding. We ship in recyclable American-made mailers. 100% money-back guarantee on all orders.

Hardcover. Condition: Very Good. Dust Jacket Condition: Very Good. Text is unmarked; pages are bright, though the page edges are a bit age toned. Binding is sturdy. Dust jacket is lightly edge worn and lightly shelf rubbed.

Condition: New. Brand New ! Fast Delivery This is an International Edition and ship within 24-48 hours. Deliver by FedEx and Dhl, & Aramex, UPS, & USPS and we do accept APO and PO BOX Addresses. Order can be delivered worldwide within 6-10 days and we do have flat rate for up to 2LB. Extra shipping charges will be requested if the Book weight is more than 5 LB. This Item May be shipped from India, United states & United Kingdom. Depending on your location and availability.…

Soft cover. Condition: Good. No jacket. Cover is lightly faded, worn, and soiled. Outer corners of the book are creased, affecting covers and pages. Crease is much more significant on top corner. Inside pages are clean and unmarked.

Condition: Good. Envoi rapide livre en très bon état avec sa jaquette (défraîchie) intérieur propre. in8. 1974. Cartonné jaquette. Good.

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Soft cover. Condition: New. Contents: Preface. 1. Inner product spaces. 2. Normed spaces. 3. Distance and approximation. 4. Continuity and compactness. 5. Banach spaces. 6. The contraction principle. 7. The Lebesgue spaces. 8. Hilbert space fundamentals. 9. Approximation theory and Fourier analysis. 10. Sobolev spaces and the Poisson problem. 11. Operator theory I. 12. Operator theory II. 13. Spectral theory of compact self-adjoint operators. 14. Applications of the spectral theorem. 15. Baire s theorem and its consequences. 16. Duality and the Hahn-Banach theorem. Historical remarks. Appendices. Bibliography. This book introduces functional analysis at an elementary level without assuming any background in real analysis, for example on metric spaces or Lebesgue integration. It focuses on concepts and methods relevant in applied contexts such as variational methods on Hilbert spaces, Neumann series, eigenvalue expansions for compact self-adjoint operators, weak differentiation and Sobolev spaces on intervals, and model applications to differential and integral equations. Beyond that, the final chapters on the uniform boundedness theorem, the open mapping theorem and the Hahn Banach theorem provide a stepping-stone to more advanced texts. The exposition is clear and rigorous, featuring full and detailed proofs. Many examples illustrate the new notions and results. Each chapter concludes with a large collection of exercises, some of which are referred to in the margin of the text, tailor-made in order to guide the student digesting the new material. Optional sections and chapters supplement the mandatory parts and allow for modular teaching spanning from basic to honors track level. …

Hardcover. Condition: Fine. Dust Jacket Condition: Good. 334 pages. Unmarked fine.

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Hard cover. Condition: Very good. No jacket. Corners of boards and spine are lightly bumped, but binding is tight. Inside is clean and unmarked.

HRD. Condition: New. New Book. Shipped from UK. Established seller since 2000.

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Paperback. Condition: New. While there is a plethora of excellent, but mostly "tell-it-all'' books on the subject, this one is intended to take a unique place in what today seems to be a still wide open niche for an introductory text on the basics of functional analysis to be taught within the existing constraints of the standard, for the United States, one-semester graduate curriculum (fifteen weeks with two seventy-five-minute lectures per week).? The book consists of seven chapters and an appendix taking the reader from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), through the basics of linear operators and functionals, the three fundamental principles (the Hahn-Banach Theorem, the Uniform Boundedness Principle, the Open Mapping Theorem and its equivalents: the Inverse Mapping and Closed Graph Theorems) with their numerous profound implications and certain interesting applications, to the elements of the duality and reflexivity theory. Chapter 1 outlines some necessary preliminaries, while the Appendix gives a concise discourse on the celebrated Axiom of Choice, its equivalents (the Hausdorff Maximal Principle, Zorn's Lemma, and Zermello's Well-Ordering Principle), and ordered sets.? Being designed as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. It contains 112 Problems, which are indispensable for understanding and moving forward. Many important statements are given as problems, a lot of these are frequently referred to and used in the main body. There are also 376 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in necessary details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problem and exercises being supplied with "existential'' hints.? The book is generous on Examples and contains numerous Remarks accompanying every definition and virtually each statement to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential.?? The prerequisites are set intentionally quite low, the students not being assumed to have taken graduate courses in real or complex analysis and general topology, to make the course accessible and attractive to a wider audience of STEM (science, technology, engineering, and mathematics) graduate students or advanced undergraduates with a solid background in calculus and linear algebra. With proper attention given to applications, plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester graduate course on the fundamentals of functional analysis for students in mathematics, physics, computer science, and engineering. ContentsPreliminariesMetric SpacesNormed Ve.…

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hardcover. Condition: VeryGood. A copy that may have been read, very minimal wear and tear. May have a remainder mark.

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