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P-Adic Numbers, Ultrametric Analysis, and Applications, 2009
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1996
This chapter, and part of the next, are devoted to a result which can be viewed either as an approximation theorem, or as a theorem characterizing the kernel of a trace operator for arbitrary sets. In the present chapter we treat the case of Sobolev spaces W m,p (R N ) for integer m and 1 < p < ∞.
David R. Adams, Lars Inge Hedberg
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This chapter, and part of the next, are devoted to a result which can be viewed either as an approximation theorem, or as a theorem characterizing the kernel of a trace operator for arbitrary sets. In the present chapter we treat the case of Sobolev spaces W m,p (R N ) for integer m and 1 < p < ∞.
David R. Adams, Lars Inge Hedberg
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2011
This chapter is devoted to an approximation theorem that allows certain adjustments of the bonding mappings in an inverse limit sequence without altering the topology of the inverse limit. We apply this fundamental result to show that if f is a mapping of an interval J onto itself that is the union of two monotone maps from nonoverlapping subintervals ...
W. T. Ingram, William S. Mahavier
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This chapter is devoted to an approximation theorem that allows certain adjustments of the bonding mappings in an inverse limit sequence without altering the topology of the inverse limit. We apply this fundamental result to show that if f is a mapping of an interval J onto itself that is the union of two monotone maps from nonoverlapping subintervals ...
W. T. Ingram, William S. Mahavier
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Classical Approximation Theorems
1976Let X be a compact Hausdorff space. Let 𝔄 be a subalgebra of C R (X) which contains the constants.
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2019
After motivating and presenting the statement of Luck’s approximation theorem, we prepare the proof with a detailed synopsis of spectral calculus for Banach-, C∗-, and von Neumann algebras. The proof is then presented in a manner that emphasizes the two main ingredients: weak convergence of spectral measures and the logarithmic bound on spectral ...
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After motivating and presenting the statement of Luck’s approximation theorem, we prepare the proof with a detailed synopsis of spectral calculus for Banach-, C∗-, and von Neumann algebras. The proof is then presented in a manner that emphasizes the two main ingredients: weak convergence of spectral measures and the logarithmic bound on spectral ...
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