MHB What Else Can the Poisson Kernel Achieve Beyond the Dirichlet Problem?

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What is the significance of the Poisson kernel (besides solving the Dirichlet problem)?

What is the Poisson's role in solving the Dirichlet problem? I know it is the solution but what is meant by its role?
 
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dwsmith said:
What is the significance of the Poisson kernel (besides solving the Dirichlet problem)?

Perhaps >>this<< might interest you. It describes the applications of Poisson's Kernel in operator theory and harmonic analysis.
 

Thread '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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