Titlebook: An Introduction to Ultrametric Summability Theory; P.N. Natarajan Book 2015Latest edition The Editor(s) (if applicable) and The Author(s),

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,Die Zul?ssigkeit der ?rzte-GmbH, . being prime and prove that any valuation of . (the field of rational numbers) is either the trivial valuation, a .-adic valuation or a power of the usual absolute value, where the power is positive and less than or equal to 1. We discuss equivalent valuations too.

入會(huì)

https://doi.org/10.1007/b138607ic set up?too. However, the Hahn–Banach theorem fails to hold. To salvage the Hahn–Banach theorem, the concept of a “spherically complete field” is introduced and Ingleton’s version of the Hahn–Banach theorem is proved. The classical “convexity” does not work in the ultrametric set up and it is repl

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,Die Zul?ssigkeit der ?rzte-GmbH,n the topic) to the present. In the present chapter, Silverman–Toeplitz theorem is proved using the “sliding-hump method”. Schur’s theorem and Steinhaus theorem also find a mention. Core of a sequence and Knopp’s core theorem is discussed. It is proved that certain Steinhaus-type theorems fail to ho

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https://doi.org/10.1007/b138607In this chapter, we discuss some arithmetic and analysis in the .-adic field. We also introduce the concepts of differentiability and derivatives in ultrametric analysis and briefly indicate how ultrametric calculus is different from our usual calculus.

CAPE

,Die Zul?ssigkeit der ?rzte-GmbH,In this chapter, we introduce the N?rlund and the Weighted Mean methods in the ultrametric set-up and their properties are elaborately discussed. We also show that the Mazur–Orlicz theorem and Brudno’s theorem fail to hold in the ultrametric case.

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https://doi.org/10.1007/978-3-642-68700-6In the current chapter, we introduce the N?rlund method and the Weighted Mean method for double sequences and establish many of their properties.

名義上

Some Arithmetic and Analysis in ,; Derivatives in Ultrametric Analysis,In this chapter, we discuss some arithmetic and analysis in the .-adic field. We also introduce the concepts of differentiability and derivatives in ultrametric analysis and briefly indicate how ultrametric calculus is different from our usual calculus.