ANALYSIS ON GROUPS: WEAK TOPOLOGIES Recall that a topological vector space is, formally, a pair (E, S ), but that we typically just refer to E when no confusion can arise from this. In this note, confusion can arise! (Bu

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ANALYSIS ON GROUPS: THE HAHN-BANACH THEOREM(S) A topological vector space is by denition a vector space E with a (Hausdor) topology S such that the vector space operations are continuous: that is, the maps E × E → E

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• Functional analysis
• Linear algebra
• Operator theory
• Topological vector spaces
• Hahn–Banach theorem
• Banach spaces
• Normed vector space
• Vector space
• Locally convex topological vector space
• Algebra
• Mathematical analysis
• Mathematics

Khan_mono_LTSCVF-(6 Aprilspellingchecked.dvi

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• Topological vector spaces
• Liaqat Ali Khan
• Locally convex topological vector space
• Tychonoff space
• Compact-open topology
• Topological space
• Locally compact space
• Vector space
• Topological group
• Topology
• General topology
• Mathematics

C k spaces and spaces of test functions Jordan Bell Department of Mathematics, University of Toronto April 10, 2014

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• Sobolev spaces
• Locally convex topological vector space
• Ordinal number
• Continuous function
• Functional analysis
• Operator theory
• Fréchet space
• Mathematical analysis
• Mathematics
• Topological vector spaces

Test functions, distributions, and Sobolev’s lemma Jordan Bell Department of Mathematics, University of Toronto May 22, 2014

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• Mathematical analysis
• Mathematics
• Spectral theory of ordinary differential equations
• Linear temporal logic
• Constructible universe
• Locally convex topological vector space
• Operator theory

Journal of Computational and Applied Mathematics–227 www.elsevier.com/locate/cam Numerical solution of the Minkowski problem a

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• Convex analysis
• Convex function
• Convex hull
• Vector space
• Convex set
• Continuous function
• Spherical harmonics
• Locally convex topological vector space
• Shapley–Folkman lemma
• Mathematical analysis
• Mathematics
• Algebra

The Fr´echet space of holomorphic functions on the unit disc Jordan Bell Department of Mathematics, University of Toronto April 3, 2014

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• Topological vector spaces
• Topology
• Linear algebra
• Functional analysis
• Locally convex topological vector space
• Norm
• Local boundedness
• Continuous function
• Minkowski functional
• Mathematics
• Algebra
• Mathematical analysis

The weak topology of locally convex spaces and the weak-* topology of their duals Jordan Bell Department of Mathematics, University of Toronto April 3, 2014

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• Functional analysis
• Banach–Alaoglu theorem
• Locally convex topological vector space
• Weak topology
• Topological vector space
• Reflexive space
• Hahn–Banach theorem
• Uniform boundedness principle
• Bounded set
• Mathematical analysis
• Mathematics
• Topology

The Legendre transform Jordan Bell Department of Mathematics, University of Toronto April 25, 2014

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• Locally convex topological vector space
• Calculus of variations
• Fourier transform
• Legendre transformation
• Partial differential equation
• Constructible universe
• Spectral theory of ordinary differential equations
• Linear temporal logic
• Mathematical analysis
• Mathematics
• Fourier analysis

Accelerated Training of Max-Margin Markov Networks with Kernels Xinhua Zhang1 , Ankan Saha2 , and S.V.N. Vishwanathan3 1 Department of Computing Science, University of Alberta, Edmonton, Canada

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• Distribution
• Lie algebras
• Proof theory
• Root system
• Locally convex topological vector space
• Mathematical analysis
• Functional analysis
• Constructible universe