Properties of the Bochner–Martinelli Integral and the Logarithmic Residue Formula

Alexander M. Kytmanov and Simona G. Myslivets
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Alexander M. Kytmanov: Siberian Federal University, Institute of Mathematics and Computer Science
Simona G. Myslivets: Siberian Federal University, Institute of Mathematics and Computer Science

Chapter Chapter 2 in Multidimensional Integral Representations, 2015, pp 21-74 from Springer

Abstract: Abstract In this chapter, we will consider the boundary behavior of the Bochner–Martinelli integral. Most of the statements have been collected in the book (Kytmanov, The Bochner–Martilnelli Integral and Its Applications. Birkhäuser Verlag, Basel, 1995). Some of these results can be obtained from the general theory of integral operators. But we seek to provide independent and more elementary proofs thereof. Since many of them will be used in the subsequent chapters, we decided to reproduce these in the book. The last section of this chapter contains the results of possible connection of the holomorphic continuation of functions with the homogeneous $$\bar{\partial }$$ -Neumann problem, emphasizing the relationship between the harmonic and complex analysis in $$\mathbb{C}^{n}$$ .

Keywords: Differential Form; Neumann Problem; Tangent Cone; Boundary Behavior; Lebesgue Point (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-21659-1_2

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DOI: 10.1007/978-3-319-21659-1_2

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