The ISAAC (International Society for Analysis, its Applications and Computation) Congress, which has been held every second year since 1997, covers the major progress in analysis, applications and computation in recent years. In this proceedings volume, plenary lectures highlight the recent research results, while 17 sessions organized by well-known specialists reflect the state of the art of important subfields. This volume concentrates on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, inverse problems, functional differential and difference equations and integrable systems.
The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics.
The emphasis of the two volumes is on complex analysis with classical topics such as value distribution, and modern topics such as complex dynamics, both in one and several complex variables; the application of complex analysis to partial differential equations and integral equations and its generalization to quaternionic and Clifford analysis; new results from real and functional analysis, numerical and computational mathematics; and areas in applied mathematics such as acoustics and computational biology. Audience: Researchers, especially those working in real and complex analysis, in numerical analysis, and in mathematical physics.
International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors. The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O Besov, V Burenkov and R P Gilbert on the occasion of their anniversaries.
The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting. Contents: .: Volume 1: Function Spaces and Fractional Calculus (V I Burenkov & S Samko); Asymptotic Decomposition (Methods of Small Parameters, Averaging Theory) (J A Dubinski); Integral Transforms and Applications (S Saitoh et al.); Analytic Functionals, Hyperfunctions and Generalized Functions (M Morimoto & H Komatsu); Geometric Function Theory (G Kohr & M Kohr); omplex Function Spaces (R Aulaskari & I Laine); Value Distribution Theory and Complex Dynamics (C C Yang); Clifford Analysis (K Grlebeck et al.); Octonions (T Dray & C Monogue); Nonlinear Potential Theory (O Martio); Classical and Fine Potential Theory, Holomorphic and Finely Holomorphic Functions (P Tamrazov); Differential Geometry and Control Theory for PDEs (B Gulliver et al.); Differential Geometry and Quantum Physics (-); Dynamical Systems (B Fiedler); Attractors for Partial Differential Equations (G Raugel); Spectral Theory of Differential Operators (B Vainberg); Pseudodifferential Operators, Quantization and Signal Analysis (M W Wong); Microlocal Analysis (B-W Schulze & M Korey); Volume 2: Complex and Functional Analytic Methods in PDEs (A Cialdea et al.); Geometric Properties of Solutions of PDEs (R Magnanini); Qualitative Properties of Solutions of Hyperbolic and SchrAdinger Equations (M Reissig & K Yagdjian); Homogenization Moving Boundaries and Porous Media (A Bourgeat & R P Gilbert); Constructive Methods in Applied Problems (P Krutitskii); Waves in Complex Media (R P Gilbert & A Wirgin); Nonlinear Waves (I Lasiecka & H Koch); Mathematical Analysis of Problems in Solid Mechanics (K Hackl & X Li); Direct and Inverse Scattering (L Fishman); Inverse Problems (G N Makrakis et al.); Mathematical Methods in Non-Destructive Evaluation and Non-Destructive Testing (A Wirgin); Numerical Methods for PDEs, Systems and Optimization (A Ben-Israel & I Herrera). Readership: Graduate students and researchers in real, complex, numerical analysis, as well as mathematical physics.
This book is the Proceedings of the Second ISAAC Congress. ISAAC is the acronym of the International Society for Analysis, its Applications and Computation. The president of ISAAC is Professor Robert P. Gilbert, the second named editor of this book, e-mail: gilbert@math.udel.edu. The Congress is world-wide valued so highly that an application for a grant has been selected and this project has been executed with Grant No. 11-56 from *the Commemorative Association for the Japan World Exposition (1970). The finance of the publication of this book is exclusively the said Grant No. 11-56 from *. Thus, a pair of each one copy of two volumes of this book will be sent to all contributors, who registered at the Second ISAAC Congress in Fukuoka, free of charge by the Kluwer Academic Publishers. Analysis is understood here in the broad sense of the word, includ ing differential equations, integral equations, functional analysis, and function theory. It is the purpose of ISAAC to promote analysis, its applications, and its interaction with computation. With this objective, ISAAC organizes international Congresses for the presentation and dis cussion of research on analysis. ISAAC welcomes new members and those interested in joining ISAAC are encouraged to look at the web site http://www .math. udel.edu/ gilbert/isaac/index.html vi and http://www.math.fu-berlin.de/ rd/ ag/isaac/newton/index.html.
This collection of survey articles gives and idea of new methods and results in real and complex analysis and its applications. Besides several chapters on hyperbolic equations and systems and complex analysis, potential theory, dynamical systems and harmonic analysis are also included. Newly developed subjects from power geometry, homogenization, partial differential equations in graph structures are presented and a decomposition of the Hilbert space and Hamiltonian are given. Audience: Advanced students and scientists interested in new methods and results in analysis and applications.
The emphasis of the two volumes is on complex analysis with classical topics such as value distribution, and modern topics such as complex dynamics, both in one and several complex variables; the application of complex analysis to partial differential equations and integral equations and its generalization to quaternionic and Clifford analysis; new results from real and functional analysis, numerical and computational mathematics; and areas in applied mathematics such as acoustics and computational biology. Audience: Researchers, especially those working in real and complex analysis, in numerical analysis, and in mathematical physics.
Plenary lectures. 1. Evaluation of Sylvester type determinants using orthogonal polynomials / R. Askey. 2. Geometric analysis on subRiemannian manifolds / O. Calin, D. C. Chang and P. Greiner. 3. A survey of Hardy type theorems / S. Thangavelu -- Approximation theory. 4. Optimal sk-spline approximation of Sobolev's classes on the 2-sphere / C. Grandison and A. Kushpel. 5. sk-spline approximation on the Torus / A. Kushpel. 6. Entropy numbers of Sobolev and Besov classes on homogeneous spaces / A. Kushpel and S. Tozoni. 7. Operator equations and best approximation problems in reproducing kernel Hilbert spaces with Tikhonov regularization / S. Saitoh, T. Matsuura and M. Asaduzzaman -- Banach apaces of analytic functions. 8. Finite Fourier transforms and the zeros of the Riemann [symbol]-function / G. Csordas and C. C. Yang. 9. B[symbol], Q[symbol] spaces and harmonic majorants / E. Ramírez de Arellano, L. F. Reséndis O. and L. M. Tovar S. 10. The (t,[symbol])-lattice and decomposition theory for function spaces / Irfan Ul-haq and Zhijian Wu -- Boundary value problems and integral equations. 11. On a generalization of the N. A. Davydov theorem / O. F. Gerus and M. Shapiro. 12. Dual integral equations method for some mixed boundary value problems / J. M. Rappoport. 13. One parameter-dependent nonlinear elliptic boundary value problems arising in population dynamics / K. Umezu -- Complex and functional analytic methods in partial differential equations. 14. Combined integral representations / H. Begehr. 15. Remarks on quantum differential operators / R. Carroll. 16. The inverse monodromy problem in a class of Knizhnik-Zamolodchikov equations / V. Golubeva. 17. Reduction of two dimensional Neumann and mixed boundary value problems to Dirichlet boundary value problems / M. Jahanshahi. 18. Lipschitz type inequalities for a domain dependent Neumann Eigenvalue problem for the Laplace operator / Pier Domenico Lamberti and Massimo Lanza de Cristoforis. 19. Half Robin problems for the Dirac operator in the unit ball of R[symbol](m[symbol]3) / Zhenyuan Xu -- Harmonic analysis and partial differential equations. 20. Problems related to the analytic representation of tempered distributions / C. Carton-Lebrun. 21. Strong unique continuation for generalized Baouendi-Grushin operators / N. Garofalo and D. Vassilev. 22. Schoenberg's theorem for positive definite functions on Heisenberg groups / J. Kim and M. W. Wong. 23. Weak and strong solutions for pseudo-differential operators / M. W. Wong -- Hemivariational inequalities and applications. 24. Comparison results for quasilinear elliptic hemivariational inequalities / S. Carl. 25. Hemivariational inequalities modeling dynamic viscoelastic contact problems with friction / S. Migórski. 26. Sensitivity analysis for generalized variational and hemivariational inequalities / B. S. Mordukhovich -- Hyperbolic problems : degeneracies, nonlinearities and global existence. 27. A smoothing property of Schrodinger equations and a global existence result for derivative nonlinear equations / M. Sugimoto and M. Ruzhansky. 28. Existence and blow up for a wave equation with a cubic convolution / K. Tsutaya. 29. Zeros and signs of solutions for some reaction-diffusion systems / H. Uesaka -- Inverse problems. 30. Constructions of approximate solutions for linear differential equations by reproducing kernels and inverse problems / M. Asaduzzaman, T. Matsuura and S. Saitoh. 31. Ultrasound as a diagnostic tool to determine osteoporosis / J. L. Buchanan, R. P. Gilbert and Y. Xu. 32. Remarks on quantum KdV / R. Carroll. 33. A mathematical model of ductal carcinoma in situ and its characteristic patterns / Y. Xu -- Nonlinear analysis and applications. 34. Classical dynamics of quantum variations / M. Kondratieva and S. Sadov -- Orthogonal polynomials and special functions. 35. On the zeros of a transcendental function / M. V. DeFazio and M. E. Muldoon. 36. Evaluation of Sylvester type determinants using block-triangularization / O. Holtz. 37. Square summability with geometric weight for classical orthogonal expansions / D. Karp. 38. The first positive zeros of cylinder functions and of their derivatives / L. Lorch -- Reproducing kernels and related topics. 39. Bergman kernel for complex harmonic functions on some balls / K. Fujita. 40. Applications of reproducing kernels to best appoximations, Tikhonov regularizations and inverse problems / S. Saitoh. 41. Equality conditions for general norm inequalities in reproducing kernel Hilbert spaces / A. Yamada -- Time-frequency analysis, wavelets and applications. 42. Comparing multiresolution SVD with other methods for image compression / R. Ashino ... [et al.]. 43. Non-translation-invariance in principal shift-invariant spaces / J. A. Hogan and J. D. Lakey. 44. Time-frequency spectra of music / J. S. Walker and A. J. Potts -- Toeplitz-like structures in analysis and applied sciences. 45. Dynamics of spectra of Toeplitz operators / S. Grudsky and N. Vasilevski. 46. Operator equalities for singular integral operators and their applications / O. Karelin -- Value distributions of complex functions, generalizations and related topics. 47. On sets of range uniqueness for entire functions / M. T. Alsugaray. 48. Analytic mappings in the tree Mult(K[x]) / K. Boussaf, A. Escassut and N. Maïnetti. 49. Using level curves to count non-real zeros of f" / S. Edwards. 50. The functional equation P(f) = Q(g) in a p-Adic field / A. Escassut and C. C. Yang. 51. Conjectures and counterexamples in dynamics of rational semigroups / R. Stankewitz, T. Sugawa and H. Sumi
The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
The ISAAC (International Society for Analysis, its Applications and Computation) Congress, which has been held every second year since 1997, covers the major progress in analysis, applications and computation in recent years. In this proceedings volume, plenary lectures highlight the recent research results, while 17 sessions organized by well-known specialists reflect the state of the art of important subfields. This volume concentrates on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, inverse problems, functional differential and difference equations and integrable systems.
The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting. Contents: .: Volume 1: Function Spaces and Fractional Calculus (V I Burenkov & S Samko); Asymptotic Decomposition (Methods of Small Parameters, Averaging Theory) (J A Dubinski); Integral Transforms and Applications (S Saitoh et al.); Analytic Functionals, Hyperfunctions and Generalized Functions (M Morimoto & H Komatsu); Geometric Function Theory (G Kohr & M Kohr); omplex Function Spaces (R Aulaskari & I Laine); Value Distribution Theory and Complex Dynamics (C C Yang); Clifford Analysis (K Grlebeck et al.); Octonions (T Dray & C Monogue); Nonlinear Potential Theory (O Martio); Classical and Fine Potential Theory, Holomorphic and Finely Holomorphic Functions (P Tamrazov); Differential Geometry and Control Theory for PDEs (B Gulliver et al.); Differential Geometry and Quantum Physics (-); Dynamical Systems (B Fiedler); Attractors for Partial Differential Equations (G Raugel); Spectral Theory of Differential Operators (B Vainberg); Pseudodifferential Operators, Quantization and Signal Analysis (M W Wong); Microlocal Analysis (B-W Schulze & M Korey); Volume 2: Complex and Functional Analytic Methods in PDEs (A Cialdea et al.); Geometric Properties of Solutions of PDEs (R Magnanini); Qualitative Properties of Solutions of Hyperbolic and SchrAdinger Equations (M Reissig & K Yagdjian); Homogenization Moving Boundaries and Porous Media (A Bourgeat & R P Gilbert); Constructive Methods in Applied Problems (P Krutitskii); Waves in Complex Media (R P Gilbert & A Wirgin); Nonlinear Waves (I Lasiecka & H Koch); Mathematical Analysis of Problems in Solid Mechanics (K Hackl & X Li); Direct and Inverse Scattering (L Fishman); Inverse Problems (G N Makrakis et al.); Mathematical Methods in Non-Destructive Evaluation and Non-Destructive Testing (A Wirgin); Numerical Methods for PDEs, Systems and Optimization (A Ben-Israel & I Herrera). Readership: Graduate students and researchers in real, complex, numerical analysis, as well as mathematical physics.
Clifford analysis has blossomed into an increasingly relevant and fashionable area of research in mathematical analysis-it fits conveniently at the crossroads of many fundamental areas of research, including classical harmonic analysis, operator theory, and boundary behavior. This book presents a state-of-the-art account of the most recent developments in the field of Clifford analysis with contributions by many of the field's leading researchers.
Proceedings of Sessions from the First Congress of the International Society for Analysis, Applications and Computing held in Newark, Delaware, June, 2-, 1997
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