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Author  Title  Accn#  Year  Item Type  Claims 
1 
Hannesdottir, Holmfridur Sigridar 
What is the i?? for the Smatrix? 
I12258 
2022 
Book 

2 
Singh, S.P 
Approximation Theory and Spline Functions 
I05075 
1984 
eBook 

3 
Singh, S.P 
Approximation Theory, Wavelets and Applications 
I03623 
1995 
eBook 

4 
Singh, S.P 
Approximation Theory, Spline Functions and Applications 
I03435 
1992 
eBook 

5 
Fuglede, B 
Approximation by Solutions of Partial Differential Equations 
I01980 
1992 
eBook 

6 
GowriSankaran, K 
Classical and Modern Potential Theory and Applications 
I00354 
1994 
eBook 


1.


Title  What is the i?? for the Smatrix? 
Author(s)  Hannesdottir, Holmfridur Sigridar;Mizera, Sebastian 
Publication  Cham, 1. Imprint: Springer
2. Springer International Publishing, 2022. 
Description  VI, 165 p. 39 illus., 37 illus. in color : online resource 
Abstract Note  This book provides a modern perspective on the analytic structure of scattering amplitudes in quantum field theory, with the goal of understanding and exploiting consequences of unitarity, causality, and locality. It focuses on the question: Can the Smatrix be complexified in a way consistent with causality? The affirmative answer has been well understood since the 1960s, in the case of 2???2 scattering of the lightest particle in theories with a mass gap at low momentum transfer, where the Smatrix is analytic everywhere except at normalthreshold branch cuts. We ask whether an analogous picture extends to realistic theories, such as the Standard Model, that include massless fields, UV/IR divergences, and unstable particles. Especially in the presence of light states running in the loops, the traditional i?? prescription for approaching physical regions might break down, because causality requirements for the individual Feynman diagrams can be mutually incompatible. We demonstrate that such analyticity problems are not in contradiction with unitarity. Instead, they should be thought of as finitewidth effects that disappear in the idealized 2???2 scattering amplitudes with no unstable particles, but might persist at higher multiplicity. To fix these issues, we propose an i??like prescription for deforming branch cuts in the space of Mandelstam invariants without modifying the analytic properties of the physical amplitude. This procedure results in a complex strip around the real part of the kinematic space, where the Smatrix remains causal. We illustrate all the points on explicit examples, both symbolically and numerically, in addition to giving a pedagogical introduction to the analytic properties of the perturbative Smatrix from a modern point of view. To help with the investigation of related questions, we introduce a number of tools, including holomorphic cutting rules, new approaches to dispersion relations, as well as formulae for local behavior of Feynman integrals near branch points. This book is well suited for anyone with knowledge of quantum field theory at a graduate level who wants to become familiar with the complexanalytic structure of Feynman integrals 
ISBN,Price  9783031182587 
Keyword(s)  1. APPROXIMATION THEORY
2. Approximations and Expansions
3. EBOOK
4. EBOOK  SPRINGER
5. Elementary particles (Physics)
6. Elementary Particles, Quantum Field Theory
7. Functions of a Complex Variable
8. FUNCTIONS OF COMPLEX VARIABLES
9. PARTICLE PHYSICS
10. PARTICLES (NUCLEAR PHYSICS)
11. QUANTUM FIELD THEORY

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I12258 


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2.


Title  Approximation Theory and Spline Functions 
Author(s)  Singh, S.P;Burry, J.H.W;Watson, B 
Publication  Dordrecht, Springer Netherlands, 1984. 
Description  IX, 485 p : online resource 
Abstract Note  A NATO Advanced Study Institute on Approximation Theory and Spline Functions was held at Memorial University of Newfoundland during August 22September 2, 1983. This volume consists of the Proceedings of that Institute. These Proceedings include the main invited talks and contributed papers given during the Institute. The aim of these lectures was to bring together Mathematicians, Physicists and Engineers working in the field. The lectures covered a wide range including ~1ultivariate Approximation, Spline Functions, Rational Approximation, Applications of Elliptic Integrals and Functions in the Theory of Approximation, and Pade Approximation. We express our sincere thanks to Professors E. W. Cheney, J. Meinguet, J. M. Phillips and H. Werner, members of the International Advisory Committee. We also extend our thanks to the main speakers and the invi ted speakers, whose contri?? butions made these Proceedings complete. The Advanced Study Institute was financed by the NATO Scientific Affairs Division. We express our thanks for the generous support. We wish to thank members of the Department of Mathematics and Statistics at MeMorial University who willingly helped with the planning and organizing of the Institute. Special thanks go to Mrs. Mary Pike who helped immensely in the planning and organizing of the Institute, and to Miss Rosalind Genge for her careful and excellent typing of the manuscript of these Proceedings 
ISBN,Price  9789400964662 
Keyword(s)  1. ANALYSIS
2. Analysis (Mathematics)
3. APPROXIMATION THEORY
4. Approximations and Expansions
5. EBOOK
6. EBOOK  SPRINGER
7. MATHEMATICAL ANALYSIS

Item Type  eBook 
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Call#  Status  Issued To  Return Due On  Physical Location 
I05075 


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3.


Title  Approximation Theory, Wavelets and Applications 
Author(s)  Singh, S.P 
Publication  Dordrecht, Springer Netherlands, 1995. 
Description  XXIV, 572 p : online resource 
Abstract Note  Approximation Theory, Wavelets and Applications draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research. The main topics covered include constructive multivariate approximation, theory of splines, spline wavelets, polynomial and trigonometric wavelets, interpolation theory, polynomial and rational approximation. Among the scientific applications were denoising using wavelets, including the denoising of speech and images, and signal and digital image processing. In the area of the approximation of functions the main topics include multivariate interpolation, quasiinterpolation, polynomial approximation with weights, knot removal for scattered data, convergence theorems in Pad?? theory, Lyapunov theory in approximation, Neville elimination as applied to shape preserving presentation of curves, interpolating positive linear operators, interpolation from a convex subset of Hilbert space, and interpolation on the triangle and simplex. Wavelet theory is growing extremely rapidly and has applications which will interest readers in the physical, medical, engineering and social sciences 
ISBN,Price  9789401585774 
Keyword(s)  1. ANALYSIS
2. Analysis (Mathematics)
3. APPROXIMATION THEORY
4. Approximations and Expansions
5. EBOOK
6. EBOOK  SPRINGER
7. FUNCTIONAL ANALYSIS
8. INTEGRAL TRANSFORMS
9. Integral Transforms, Operational Calculus
10. MATHEMATICAL ANALYSIS
11. MATHEMATICS
12. Mathematics, general
13. Operational calculus
14. OPERATOR THEORY

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Call#  Status  Issued To  Return Due On  Physical Location 
I03623 


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4.


Title  Approximation Theory, Spline Functions and Applications 
Author(s)  Singh, S.P 
Publication  Dordrecht, Springer Netherlands, 1992. 
Description  XVI, 479 p : online resource 
Abstract Note  These are the Proceedings of the NATO Advanced Study Institute on Approximation Theory, Spline Functions and Applications held in the Hotel villa del Mare, Maratea, Italy between April 28,1991 and May 9, 1991. The principal aim of the Advanced Study Institute, as reflected in these Proceedings, was to bring together recent and uptodate developments of the subject, and to give directions for future research. Amongst the main topics covered during this Advanced Study Institute is the subject of uni?? variate and multivariate wavelet decomposition over spline spaces. This is a relatively new area in approximation theory and an increasingly impor?? tant subject. The work involves key techniques in approximation theory?? cardinal splines, Bsplines, EulerFrobenius polynomials, spline spaces with nonuniform knot sequences. A number of scientific applications are also highlighted, most notably applications to signal processing and digital im?? age processing. Developments in the area of approximation of functions examined in the course of our discussions include approximation of periodic phenomena over irregular node distributions, scattered data interpolation, Pade approximants in one and several variables, approximation properties of weighted Chebyshev polynomials, minimax approximations, and the Strang?? Fix conditions and their relation to radial functions. I express my sincere thanks to the members of the Advisory Commit?? tee, Professors B. Beauzamy, E. W. Cheney, J. Meinguet, D. Roux, and G. M. Phillips. My sincere appreciation and thanks go to A. Carbone, E. DePas?? cale, R. Charron, and B 
ISBN,Price  9789401126342 
Keyword(s)  1. ANALYSIS
2. Analysis (Mathematics)
3. APPROXIMATION THEORY
4. Approximations and Expansions
5. EBOOK
6. EBOOK  SPRINGER
7. MATHEMATICAL ANALYSIS
8. MATHEMATICS
9. Mathematics, general

Item Type  eBook 
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Call#  Status  Issued To  Return Due On  Physical Location 
I03435 


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5.


Title  Approximation by Solutions of Partial Differential Equations 
Author(s)  Fuglede, B;Goldstein, M;Haussmann, W;Hayman, W.K;Rogge, L 
Publication  Dordrecht, Springer Netherlands, 1992. 
Description  XII, 201 p : online resource 
Abstract Note  This volume consists of the proceedings of the NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations, Quadrature Formulae, and Related Topics, which was held at Hanstholm, Denmark. These proceedings include the main invited talks and contributed papers given during the workshop. The aim of these lectures was to present a selection of results of the latest research in the field. In addition to covering topics in approximation by solutions of partial differential equations and quadrature formulae, this volume is also concerned with related areas, such as Gaussian quadratures, the Pompelu problem, rational approximation to the Fresnel integral, boundary correspondence of univalent harmonic mappings, the application of the Hilbert transform in two dimensional aerodynamics, finely open sets in the limit set of a finitely generated Kleinian group, scattering theory, harmonic and maximal measures for rational functions and the solution of the classical Dirichlet problem. In addition, this volume includes some problems in potential theory which were presented in the Problem Session at Hanstholm 
ISBN,Price  9789401124362 
Keyword(s)  1. APPROXIMATION THEORY
2. Approximations and Expansions
3. EBOOK
4. EBOOK  SPRINGER
5. PARTIAL DIFFERENTIAL EQUATIONS
6. POTENTIAL THEORY
7. Potential theory (Mathematics)

Item Type  eBook 
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Accession#  
Call#  Status  Issued To  Return Due On  Physical Location 
I01980 


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6.
 
Title  Classical and Modern Potential Theory and Applications 
Author(s)  GowriSankaran, K;Bliedtner, J;Feyel, D;Goldstein, M;Hayman, W.K;Netuka, I 
Publication  Dordrecht, Springer Netherlands, 1994. 
Description  XIV, 470 p : online resource 
ISBN,Price  9789401111386 
Keyword(s)  1. ANALYSIS
2. Analysis (Mathematics)
3. APPROXIMATION THEORY
4. Approximations and Expansions
5. EBOOK
6. EBOOK  SPRINGER
7. MATHEMATICAL ANALYSIS
8. PARTIAL DIFFERENTIAL EQUATIONS
9. POTENTIAL THEORY
10. Potential theory (Mathematics)
11. PROBABILITIES
12. Probability Theory and Stochastic Processes

Item Type  eBook 
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Accession#  
Call#  Status  Issued To  Return Due On  Physical Location 
I00354 


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