Bochner
In mathematics, "Bochner" is most commonly associated with Salomon Bochner (1899-1982), a prominent mathematician known for his contributions to several areas, including harmonic analysis, probability theory, and differential geometry. Consequently, "Bochner" often appears as a prefix in the names of theorems, spaces, and other mathematical concepts related to his work.
Specifically, notable concepts named after Bochner include:
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Bochner Integral: A generalization of the Lebesgue integral to functions taking values in a Banach space. This allows integration of functions more general than real-valued functions. The Bochner integral is crucial in the study of vector-valued functions and their applications.
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Bochner Space: Generally refers to the space of Bochner integrable functions. More precisely, it refers to a function space comprised of measurable functions from a measure space into a Banach space, such that the integral of the norm of the function is finite.
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Bochner's Theorem: In harmonic analysis, this theorem provides a characterization of positive-definite functions on the real line (or more generally, on a locally compact abelian group). It states that a continuous, bounded function is positive-definite if and only if it is the Fourier-Stieltjes transform of a finite positive measure. This theorem has important applications in probability theory and signal processing.
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Bochner-Martinelli Formula: A generalization of the Cauchy integral formula to several complex variables. This formula provides a way to represent holomorphic functions in terms of an integral over the boundary of a domain in complex n-space.
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Bochner Coordinates: A specific coordinate system used in Riemannian geometry, particularly when studying Riemannian manifolds with certain symmetries.
The term "Bochner" may also appear in other mathematical contexts or in conjunction with other mathematicians' names to denote theorems or concepts arising from collaborative work. In general, the presence of "Bochner" signifies a connection to, or generalization of, the mathematical ideas developed and explored by Salomon Bochner.