Download or read book Expansions in Eigenfunctions of Selfadjoint Operators written by I͡Uriĭ Makarovich Berezanskiĭ and published by American Mathematical Soc.. This book was released on 1968 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Expansion in Eigenfunctions of Self adjoint Operators written by J. M. Berezanskii and published by . This book was released on 1968 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Expansions in Eigenfunctions of Selfadjoint Operators written by and published by . This book was released on 1968 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Selfadjoint Operators in Spaces of Functions of Infinitely Many Variables written by I_Uri_ Makarovich Berezanski_ and published by American Mathematical Soc.. This book was released on 1986-12-31 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions in the spectral theory of selfadjoint and normal operators acting in spaces of functions of infinitely many variables are studied in this book, and, in particular, the theory of expansions in generalized eigenfunctions of such operators. Both individual operators and arbitrary commuting families of them are considered. A theory of generalized functions of infinitely many variables is constructed. The circle of questions presented has evolved in recent years, especially in connection with problems in quantum field theory. This book will be useful to mathematicians and physicists interested in the indicated questions, as well as to graduate students and students in advanced university courses.
Download or read book Advanced Quantum Mechanics written by RAINER DICK and published by Springer. This book was released on 2016-07-01 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this updated and expanded second edition of a well-received and invaluable textbook, Prof. Dick emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. Advanced Quantum Mechanics, Materials and Photons can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. This second edition includes an additional 62 new problems as well as expanded sections on relativistic quantum fields and applications of quantum electrodynamics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquired an understanding of basic quantum mechanics and classical field theory, canonical field quantization is easy. Furthermore, the integrated discussion of transition amplitudes naturally leads to the notions of transition probabilities, decay rates, absorption cross sections and scattering cross sections, which are important for all experimental techniques that use photon probes.
Download or read book Expansions in Eigenfunctions of Selfadjoint Operators written by and published by . This book was released on 1968 with total page 821 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non Self Adjoint Boundary Eigenvalue Problems written by R. Mennicken and published by Elsevier. This book was released on 2003-06-26 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations. In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every n-th order differential equation is equivalent to a first order system, the main techniques are developed for systems. Asymptotic fundamental systems are derived for a large class of systems of differential equations. Together with boundary conditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10. The contour integral method and estimates of the resolvent are used to prove expansion theorems. For Stone regular problems, not all functions are expandable, and again relatively easy verifiable conditions are given, in terms of auxiliary boundary conditions, for functions to be expandable. Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such as the Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated. Key features: • Expansion Theorems for Ordinary Differential Equations • Discusses Applications to Problems from Physics and Engineering • Thorough Investigation of Asymptotic Fundamental Matrices and Systems • Provides a Comprehensive Treatment • Uses the Contour Integral Method • Represents the Problems as Bounded Operators • Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions
Download or read book Self Adjoint Operators written by W.G. Faris and published by Springer. This book was released on 2006-11-15 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Expansions in Eigenfunctions of Selfadjoint Operators written by and published by . This book was released on 1968 with total page 809 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral methods in infinite dimensional analysis 2 1995 written by I︠U︡riĭ Makarovich Berezanskiĭ and published by Springer Science & Business Media. This book was released on 1995 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operator Theory for Electromagnetics written by George W. Hanson and published by Springer Science & Business Media. This book was released on 2001-10-12 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text discusses electromagnetics from the view of operator theory, in a manner more commonly seen in textbooks of quantum mechanics. It includes a self-contained introduction to operator theory, presenting definitions and theorems, plus proofs of the theorems when these are simple or enlightening.
Download or read book Spectral Theory of Families of Self Adjoint Operators written by Anatolii M. Samoilenko and published by Springer Science & Business Media. This book was released on 1991-01-31 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with structure theorems and models for finite and countable families of self-adjoint operators, which satisfy commutative, non-commutative, Lie and more general relations. This book is useful for mathematicians and physicists whose work involves spectral theory, Lie algebras and probability theory.
Download or read book Razlozenie po sobstoennym funkciyam samosopryazennyh operatorov written by Yu.M. Berezanskii and published by . This book was released on 1965 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Real Analysis written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2008-07-11 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
Download or read book Expansions in Eigenfunctions of Selfadjoint Operators Selfadjoint Operators written by John Rose and published by . This book was released on 1968 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Application of Non Self Adjoint Operator Theory to the Singularity Expansion Method SEM and the Eigenmode Expansion Method EEM in Acoustic and Electromagnetic Problems written by Charles L. Dolph and published by . This book was released on 1980 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eigenfunction expansions for nonselfadjoint operators are important for scalar and electromagnetic wave scattering. Two methods: the Singularity Expansion Method (SEM), and the Eigenmode Expansion Method (EEM) which had been developed separately were studied. Criteria for their validity were established; moreover, the poles of the Green's function of the SEM are in 1-1 correspondence with the zeros of the eigenvalues of the EEM. A constructive numerical process for determining the poles of the Green's function was developed. Among several other results was the establishment of variational principles for the spectrum of compact nonselfadjoint operators. Another research area was the singularity behavior of eigenfunction expansions of various Green's functions in electromagnetic theory. The principal result shows that in an eigenfunction of a typical Green's function the point singularity of a Green's function is represented by a layer of surface singularity. This characteristic is analogous to the Gibbs' phenomenon where the representation of a discontinuous function by an orthogonal expansion creates the spikes which are absent in the original function. (Author).
Download or read book Problems of the Spectral Theory of Non Self Adjoint Operators written by M. V. Keldysh and published by . This book was released on 1972 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The class of non self adjoint operators, for which the unconditionally converging expansion of the eigenfunctions is correct, has not yet been fully defined (for example, it is not known whether ellipital differential operators with partial derivatives belong to this class). However, it is now clear that the spectral expansion converging on the norm is not a necessary characteristic of the general linear operator. Apparently, further development of the theory will be achieved by establishing the generalized spectral expansion. It is noted that considerable material has been accumulated in the theory of non self adjoint problems, and it is characteristic that in recent years the theory has been supplemented with a number of new and important studies. Successes have been particularly great in the area of operators with discrete spectrum. The first three sections discuss this theme. (Author).
