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 Zulässigkeit der Ärzte-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.

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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 Zulässigkeit der Ärzte-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.

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,Die Zulässigkeit der Ärzte-GmbH,In this chapter, we introduce the Nörlund 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 Nörlund method and the Weighted Mean method for double sequences and establish many of their properties.

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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.