Integral Representations and Residues in
                    Multidimensional Complex Analysis

Yuzhakov, A. P.; Aizenberg, Lev; Aizenberg, I. A.

doi:10.1090/mmono/058

Cited by 226 publications

(241 citation statements)

References 4 publications

Supporting

Mentioning

236

Contrasting

Unclassified

Order By: Relevance

“…The above series is the continuous generalization of the Lagrange series (cf [45] for the scalar case, [46] for the multi-dimensional case, [1] and Appendix D for the continuous generalization). This series is absolutely convergent if there exists a R 0 > 0 such that for all λ ∈ Γ j;k 1 2π log…”

Section: Substituting (51) (52) and (54) Into (420) We Obtainmentioning

confidence: 99%

Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas

Kozłowski¹,

Maillet²,

Slavnov³

2011

J. Stat. Mech.

View full text Add to dashboard Cite

We describe a Bethe ansatz based method to derive, starting from a multiple integral representation, the long-distance asymptotic behavior at finite temperature of the density-density correlation function in the interacting onedimensional Bose gas. We compute the correlation lengths in terms of solutions of non-linear integral equations of the thermodynamic Bethe ansatz type. Finally, we establish a connection between the results obtained in our approach with the correlation lengths stemming from the quantum transfer matrix method.

show abstract

Section: Substituting (51) (52) and (54) Into (420) We Obtainmentioning

confidence: 99%

Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas

Kozłowski¹,

Maillet²,

Slavnov³

2011

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…The theory is particularly effective in the situation of two variables, and we describe it in this case. References include [15,16,17,18]. An application to chemical reaction rate equations appears in Ref.…”

Section: Residue Methods: Theorymentioning

confidence: 99%

“…A subset of these paths forms a basis for the relative homology group H 1 (X, ∂B). Furthermore, by Alexander duality 16 , an element of H 2 (B − X) is uniquely determined by its linking numbers with these paths (indeed, with those in a basis alone). (The linking number l(c 1 , c 2 ) of a 1-cycle with a 2-cycle in a 4-ball is the intersection number of c 1 with any 3-manifold having boundary c 2 .…”

Section: Appendix : the Homology Class Of The Torus Tmentioning

confidence: 99%

Magnification relations in gravitational lensing via multidimensional residue integrals

Dalal

Rabin

2001

Journal of Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…Consider M ≤ n closed hypersurfaces S 1 , ..., S M in X that intersect as a non empty complete intersection, that is, the closed analytic subset V = M j=1 S j ⊂ X is purely (n − M )-dimensional (all its irreducible components have complex dimension n−M ). When S 1 , ..., S M are assumed to be smooth and moreover to intersect transversally, a well known construction by J. Leray [22] (see also [1]) leads to the construction (from the cohomological point of view) of the iterated Poincaré residue morphism from H p (X \ S 1 ∪ · · · ∪ S M , C) into H p−M (V, C) (paired with its dual iterated coboundary morphism) when p ≥ M . Following a currential (instead of cohomological) point of view, the construction proposed by N. Coleff and M. Herrera in [14] allows to drop the assumption about smoothness of the S j 's and the fact they intersect transversally, keeping just (for the moment) the complete intersection hypothesis.…”

Section: From Poincaré-leray To Coleff-herrera Constructionmentioning

confidence: 99%

Coleff–Herrera Currents Revisited

Vidras

Yger

2012

The Mathematical Legacy of Leon Ehrenpreis

View full text Add to dashboard Cite

In the present paper, we describe the recent approach to residue currents by M. Andersson, J. E. Björk, H. Samuelsson [2,12,13], focusing primarily on the methods inspired by analytic continuation (which were initiated in a quite primitive form in [8]). Coleff-Herrera currents (with or without poles) play indeed a crucial role in Lelong-Poincaré type factorization formulas for integration currents on reduced closed analytic sets. As revealed by local structure theorems (which could also be understood as global when working on a complete algebraic manifold due to the GAGA principle), such objects are of algebraic nature (antiholomorphic coordinates playing basically the role of "inert" constants). Thinking about division or duality problems instead of intersection ones (especially in the "improper" setting, which is certainly the most interesting), it happens then to be necessary to revisit from this point of view the multiplicative inductive procedure initiated by N. Coleff and M. Herrera in [14], this being the main objective of this presentation. In hommage to the pioneer work of Leon Ehrenpreis, to whom we are both deeply indepted, and as a tribute to him, we also suggest a currential approach to the so-called Noetherian operators, which remain the key stone in various formulations of Leon's Fundamental Principle.

show abstract

Integral Representations and Residues in Multidimensional Complex Analysis

Cited by 226 publications

References 4 publications

Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas

Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas

Magnification relations in gravitational lensing via multidimensional residue integrals

Coleff–Herrera Currents Revisited

Contact Info

Product

Resources

About