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, 1978 One approach to the solution of non-homogeneous boundary value problems is by means of the construction of functions known as Green’s functions. Historically, the concept originated with work on potential theory published by Green in 1828. Green’s work has provided the germs of a much wider formulation for solving a variety of eigenvalue, boundary ...
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2011
The Green’s function is an important tool with applications in classical as well as quantum physics (for an introduction, see particularly the book by Fetter and Walecka [5, Chap. 3], see also the book by Mahan [8]). More recently, it has been applied also to quantum-electrodynamics by Shabaev et al. [11].
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The Green’s function is an important tool with applications in classical as well as quantum physics (for an introduction, see particularly the book by Fetter and Walecka [5, Chap. 3], see also the book by Mahan [8]). More recently, it has been applied also to quantum-electrodynamics by Shabaev et al. [11].
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Journal of Mathematical Physics, 1964
A one-parameter integral representation is given for the momentum space Green's function of the nonrelativistic Coulomb problem.
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A one-parameter integral representation is given for the momentum space Green's function of the nonrelativistic Coulomb problem.
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Variation of Green's Functions
Journal of Mathematical Physics, 1966The variation of the Green's function of a linear differential operator is computed as the variation of an n-tuple integral with variable boundary. This generalization of Hadamard formula is shown to lead naturally to the method of ``invariant imbedding'' of R. Bellman.
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, 1988 In many important applications it is desirable to find an integral representation for the solution to a boundary value problem. To achieve this goal we first discuss in this chapter “nonsmooth” solutions to such problems and then show how the existence of such solutions enable us to solve our original problem.
William Miller, Mayer Humi
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2016
The focus of this chapter is a detailed analysis of two specific positive definite functions, each one defined in a fixed finite interval, centered at x = 0. Rationale: The examples serve to make explicit some of the many connections between our general theme (locally defined p.d. functions and their extensions), on the one hand; and probability theory
Steen Pedersen +2 more
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The focus of this chapter is a detailed analysis of two specific positive definite functions, each one defined in a fixed finite interval, centered at x = 0. Rationale: The examples serve to make explicit some of the many connections between our general theme (locally defined p.d. functions and their extensions), on the one hand; and probability theory
Steen Pedersen +2 more
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1985
The fascinating concept of the Green’s function is due to the insight and intuition of George Green (1793–1841), an English mathematician, whose original work was unappreciated for nearly all of his life — largely due to his unusual methodology, George Green was born in 1793 and was 44 years old when he received his degree of Bachelor of Arts in 1837 ...
George Adomian, Richard Bellman
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The fascinating concept of the Green’s function is due to the insight and intuition of George Green (1793–1841), an English mathematician, whose original work was unappreciated for nearly all of his life — largely due to his unusual methodology, George Green was born in 1793 and was 44 years old when he received his degree of Bachelor of Arts in 1837 ...
George Adomian, Richard Bellman
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1998
Green’s functions are useful in solving the first boundary value problem (Dirichlet problem) of potential theory in itself and in the case of conformal mapping of a region onto a disk. In the latter case a relationship is needed between the conformal map and Green’s function for the region.
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Green’s functions are useful in solving the first boundary value problem (Dirichlet problem) of potential theory in itself and in the case of conformal mapping of a region onto a disk. In the latter case a relationship is needed between the conformal map and Green’s function for the region.
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1992
In this chapter we derive Green’s functions useful for scattering and propagation problems. We present a thorough discussion of one-dimensional problems as well as many examples. The Green’s functions for the wave and Helmholtz equations are derived and interrelated for one, two, and three dimensions.
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In this chapter we derive Green’s functions useful for scattering and propagation problems. We present a thorough discussion of one-dimensional problems as well as many examples. The Green’s functions for the wave and Helmholtz equations are derived and interrelated for one, two, and three dimensions.
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