This book is based largely on courses that the author taught at the Feinberg Graduate School of the Weizmann Institute. It conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that the author has found to be useful in his own research and wishes that he had been exposed to as a graduate student. Roughly the first quarter of the book reviews the contents of a basic course in linear algebra, plus a little. The remaining chapters treat singular value decompositions, convexity, special classes of matrices, projections, assorted algorithms, and a number of applications. The applications are drawn from vector calculus, numerical analysis, control theory, complex analysis, convex optimization, and functional analysis. In particular, fixed point theorems, extremal problems, best approximations, matrix equations, zero location and eigenvalue location problems, matrices with nonnegative entries, and reproducing kernels are discussed. This new edition differs significantly from the second edition in both content and style. It includes a number of topics that did not appear in the earlier edition and excludes some that did. Moreover, most of the material that has been adapted from the earlier edition has been extensively rewritten and reorganized.

This monograph deals primarily with the prediction of vector valued stochastic processes that are either weakly stationary, or have weakly stationary increments, from finite segments of their past. The main focus is on the analytic counterpart of these problems, which amounts to computing projections onto subspaces of a Hilbert space of p x 1 vector valued functions with an inner product that is defined in terms of the p x p matrix valued spectral density of the process. The strategy is to identify these subspaces as vector valued de Branges spaces and then to express projections in terms of the reproducing kernels of these spaces and/or in terms of a generalized Fourier transform that is obtained from the solution of an associated inverse spectral problem. Subsequently, the projection of the past onto the future and the future onto the past is interpreted in terms of the range of appropriately defined Hankel operators and their adjoints, and, in the last chapter, assorted computations are carried out for rational spectral densities. The underlying mathematics needed to tackle this class of problems is developed in careful detail, but, to ease the reading, an attempt is made to avoid excessive generality. En route a number of results that, to the best of our knowledge, were only known for p = 1 are generalized to the case p > 1.

This largely self-contained treatment surveys, unites and extends some 20 years of research on direct and inverse problems for canonical systems of integral and differential equations and related systems. Five basic inverse problems are studied in which the main part of the given data is either a monodromy matrix; an input scattering matrix; an input impedance matrix; a matrix valued spectral function; or an asymptotic scattering matrix. The corresponding direct problems are also treated. The book incorporates introductions to the theory of matrix valued entire functions, reproducing kernel Hilbert spaces of vector valued entire functions (with special attention to two important spaces introduced by L. de Branges), the theory of J-inner matrix valued functions and their application to bitangential interpolation and extension problems, which can be used independently for courses and seminars in analysis or for self-study. A number of examples are presented to illustrate the theory.

This volume is dedicated to Bill Helton on the occasion of his sixty fifth birthday. It contains biographical material, a list of Bill's publications, a detailed survey of Bill's contributions to operator theory, optimization and control and 19 technical articles. Most of the technical articles are expository and should serve as useful introductions to many of the areas which Bill's highly original contributions have helped to shape over the last forty odd years. These include interpolation, Szegoe limit theorems, Nehari problems, trace formulas, systems and control theory, convexity, matrix completion problems, linear matrix inequalities and optimization. The book should be useful to graduate students in mathematics and engineering, as well as to faculty and individuals seeking entry level introductions and references to the indicated topics. It can also serve as a supplementary text to numerous courses in pure and applied mathematics and engineering, as well as a source book for seminars.

This book is dedicated to the memory of Israel Gohberg (1928-2009) - one of the great mathematicians of our time - who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg's mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.

J-contractive and J-inner matrix valued functions have a wide range of applications in mathematical analysis, mathematical physics, control engineering and theory of systems and networks. This book provides a comprehensive introduction to the theory of these functions with respect to the open upper half-plane, and a number of applications are also discussed. The first chapters develop the requisite background material from the geometry of finite dimensional spaces with an indefinite inner product, and the theory of the Nevanlinna class of matrix valued functions with bounded characteristic in the open upper half-plane (with attention to special subclasses). Subsequent chapters develop this theory to include associated pairs of inner matrix valued functions and reproducing kernel Hilbert spaces. Special attention is paid to the subclasses of regular and strongly regular J-inner matrix valued functions, which play an essential role in the study of the extension and interpolation problems.

This volume is dedicated to Bill Helton on the occasion of his sixty fifth birthday. It contains biographical material, a list of Bill's publications, a detailed survey of Bill's contributions to operator theory, optimization and control and 19 technical articles. Most of the technical articles are expository and should serve as useful introductions to many of the areas which Bill's highly original contributions have helped to shape over the last forty odd years. These include interpolation, Szegoe limit theorems, Nehari problems, trace formulas, systems and control theory, convexity, matrix completion problems, linear matrix inequalities and optimization. The book should be useful to graduate students in mathematics and engineering, as well as to faculty and individuals seeking entry level introductions and references to the indicated topics. It can also serve as a supplementary text to numerous courses in pure and applied mathematics and engineering, as well as a source book for seminars.

This book is dedicated to the memory of Israel Gohberg (1928-2009) - one of the great mathematicians of our time - who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg's mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.

In this issue of Oral and Maxillofacial Surgery Clinics, guest editor Harry Dym brings his considerable expertise to the topic of Clinical Pharmacology for the Oral and Maxillofacial Surgeon. Top experts in the field cover key topics such as a review of sedation agents, acute pain management, and more. Contains 17 relevant, practice-oriented topics including Emergency Drugs for the Oral and Maxillofacial Surgeon Office; Update on Medications for Oral Sedation in the Oral and Maxillofacial Surgery Office; Pharmacologic Treatment for Tempromandibular and TMJ Disorders; and more. Provides in-depth clinical reviews on Clinical Pharmacology for the Oral and Maxillofacial Surgeon, offering actionable insights for clinical practice. Presents the latest information on this timely, focused topic under the leadership of experienced editors in the field. Authors synthesize and distill the latest research and practice guidelines to create clinically significant, topic-based reviews.

This issue of Dental Clinics of North America focuses on Implant Surgery Update for the General Practitioner, and is edited by Dr. Harry Dym. Articles will include: The Medically Complex Dental Implant Patient: Controversies with Respect to Systemic Disease and Dental Implant Success and Survival; Placement of Short Implants: A Viable Alternative?; Surgical Approaches to Implant Placement in the Vertically & Horizontally Challenged Ridge; Update on Maxillary Sinus Augmentation; Implant Surgery Update for the General Practitioner; How to Avoid Life Threatening Complications Associated with Implant Surgery; All-on-4 Implant Concept Update; An Update on the Treatment of Peri-implantitis; Soft Tissue Injury in Preparation for Implants; Update on Zygomatic Implants; Prosthodontic Principles in Dental Implantology: Adjustments in a COVID-19 Pandemic-battered Economy; Guided Implant Surgery: A Technique Whose Time Has Come; Implant Material Sciences; Immediate Implants and Immediate Loading: Current Concepts; An Update on Hard Tissue Grafting Materials; and more!

This issue of Dental Clinics, edited by Harry Dym, focuses on Implant Procedures for the General Dentist. Articles will include: Basic principles of implant surgery, Maxillary sinus augmentation techniques, Surgical techniques for augmentation in the horizontally and vertically compromised alveolus, Autologous bone harvest sites, Bone morphogenic protein and its application to implant dentistry, Soft tissue augmentation for implant surgery, Immediate placement and immediate loading: Surgical technique and clinical pearls, Treatment of peri-implantitis and the failing implant, Implant related nerve injury, All on four techniques, CT-guided implant surgery, Short implants: Are they a viable option in implant dentistry?, Treatment planning for implant surgery, Surface material, implant design and osseointegration, Tissue response to implants, and more!

In this issue of Dental Clinics, guest editor Dr. Harry Dym brings his considerable expertise to the topic of Controversies in Oral and Maxillofacial Surgery. Evidence-based dentistry based on high-quality research is essential to help develop new treatments and alternative options. This issue tackles clinically relevant controversial subjects and helps present cogent, clear information for the clinician to determine the best possible solution or approach. Contains 14 relevant, practice-oriented topics, including short implants: their role in implant reconstruction; need for cone beam imaging in oral surgery and dentistry?; bisphosphonate therapy and its implications in dentistry and oral surgery; post-procedure analgesic management; controversies in the management of the sleep apnea patient; and more. Provides in-depth clinical reviews on controversies in oral and maxillofacial surgery, offering actionable insights for clinical practice. Presents the latest information on this timely, focused topic under the leadership of experienced editors in the field. Authors synthesize and distill the latest research and practice guidelines to create clinically significant, topic-based reviews.

This monograph deals primarily with the prediction of vector valued stochastic processes that are either weakly stationary, or have weakly stationary increments, from finite segments of their past. The main focus is on the analytic counterpart of these problems, which amounts to computing projections onto subspaces of a Hilbert space of p x 1 vector valued functions with an inner product that is defined in terms of the p x p matrix valued spectral density of the process. The strategy is to identify these subspaces as vector valued de Branges spaces and then to express projections in terms of the reproducing kernels of these spaces and/or in terms of a generalized Fourier transform that is obtained from the solution of an associated inverse spectral problem. Subsequently, the projection of the past onto the future and the future onto the past is interpreted in terms of the range of appropriately defined Hankel operators and their adjoints, and, in the last chapter, assorted computations are carried out for rational spectral densities. The underlying mathematics needed to tackle this class of problems is developed in careful detail, but, to ease the reading, an attempt is made to avoid excessive generality. En route a number of results that, to the best of our knowledge, were only known for p = 1 are generalized to the case p > 1.

This issue of Dental Clinics of North America focuses on Pharmacology and Therapeutics for the Dentist. Articles will include: Emergency Drugs for the Dental Office; Oral Sedation for Adult and Pediatric Dental Patients; Update on Analgesic Medication for Adult and Pediatric Dental Patients; Medication Management for TMD/TMJ Dental Patients; Medications and their Role in the Chronic Facial/Neuropathic Pain of Dental Patients; Medication Management for Xerostomia and Glossodynia in the Dental Patient; Update on Topical and Local Anesthesia Agents for Dental Patients; Current Concepts of Prophylactic Antibiotics for Dental Patients; Medication Management of Jaw Lesions for Dental Patients; Current Update on Antibiotic Therapy for Odontogenic Infections in Dental Patients; Review of Top 10 Prescribed Drugs and their Interaction with Dental Treatment; Botox: Review and Its Role in the Dental Office; Medication and the Gravid and Nursing Dental Patient; Conscious IV Sedation in Dentistry: A Review of Current Therapy; Medications to Assist in Tobacco Cessation for the Dental Patient; Topical and Systemic Drugs in the Treatment of Oral Ulcers for the Dental Patient, and more!

Guest Editors Orrett Ogle and Harry Dym present a comprehensive look at surgery of the nose and paranasal sinuses. Topics include surgical anatomy of the paranasal sinuses, instrumentation and techniques for examination of the ear, nose, throat and sinuses, imaging of the paranasal sinuses, microbiology of the paranasal sinuses, surgery of the paranasal sinuses, removal of parotid, submandibular and sublingual glands, oro-antral and oro-nasal fistulas, turbinectomy and surgery for nasal obstruction, cysts and benign tumors of paranasal sinuses, tonsillitis, peritoinsilar and lateral pharyngeal abscesses, and much more!

This Issue of Dental Clinics of North America is devoted to technological advances in dentistry.

This issue of Dental Clinics of North America focuses on Surgical and Medical Management of Common Oral Problems, and is edited by Dr. Harry Dym. Articles will include: Short Implants: An Answer to a Challenging Dilemma; Surgical Case Review Utilizing New Techniques to Treat a Complex Case; The Role of Platelet Rich Fibrin in the Dental Office; The Total Joint Prosthesis: Indications and Techniques; Peri-implantitis: Why and How to Manage; New Approaches to Pain Management; Botox and Fillers Review; Diagnosis and Treatment Approaches to a "Gummy Smile"; Role of Piezzo Surgery and Lasers in the Modern Dental Office; Intra-Oral Scanner, 3D Imaging and 3D Printing in the Dental Office; Recognizing Neuropathic Pain and Current Treatment Regimens; Zygomatic Implant Replacement; Update on Treatment of the Anti-Coagulation Patient and Hemostatic Agents; Growing Bone: Old and New Techniques Reviewed; Obstructive Sleep Apnea: A Review for the General Dentist; and more!

Linear algebra permeates mathematics, perhaps more so than any other single subject. It plays an essential role in pure and applied mathematics, statistics, computer science, and many aspects of physics and engineering. This book conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that many of us wish we had been taught as a graduate student. Roughly the first third of the book covers the basic material of a first course in linear algebra. The remaining chapters are devoted to applications drawn from vector calculus, numerical analysis, control theory, complex analysis, convexity and functional analysis. In particular, fixed point theorems, extremal problems, matrix equations, zero location and eigenvalue location problems, and matrices with nonnegative entries are discussed. Appendices on useful facts from analysis and supplementary information from complex function theory are also provided for the convenience of the reader. In this new edition, most of the chapters in the first edition have been revised, some extensively. The revisions include changes in a number of proofs, either to simplify the argument, to make the logic clearer or, on occasion, to sharpen the result. New introductory sections on linear programming, extreme points for polyhedra and a Nevanlinna-Pick interpolation problem have been added, as have some very short introductory sections on the mathematics behind Google, Drazin inverses, band inverses and applications of SVD together with a number of new exercises.