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In Kellogg published his first paper giving a direct proof of Fredholm 's inversion formula. In January of the following year he kellogg potential theory his doctorate for his dissertation Zur Theorie der Integralgleichungen und des Dirichlet'schen Kellogg potential theory on the Dirichlet problem but he remained in Germany to the end of the academic year, returning to the United States to take up the post of instructor in mathematics at Princeton.

Oliver Dimon Kellogg

During these years he published two further papers which developed from the work of his thesis. However Kellogg soon became less than happy with these papers.

Partly he had failed to answer the questions Hilbert had asked him kellogg potential theory solve though this kellogg potential theory understandable since they were much harder than Hilbert had realised.

Secondly some of Kellogg's results were kellogg potential theory and others were incorrect. Kellogg was appointed to the University of Missouri in where, despite a heavy teaching and administrative load he was able to publish impressive papers on potential theory.

Foundations of Potential Theory

In he published three papers, namely Potential functions on the boundary of their regions of definition and Double distributions and the Dirichlet problem, both in the Transactions kellogg potential theory the American Mathematical Society, and A necessary condition kellogg potential theory all the roots of an algebraic equation be real in the Annals of Mathematics.

In he published the important work Harmonic functions and Green's integral in the Transactions of the American Mathematical Society. This paper includes what today is called 'Kellogg's theorem' on harmonic and Green 's functions.

He was promoted to professor at the University of Missouri in and, in the following year, he married Edith Taylor; they had one daughter.

Reciprocity; Gauss' Theorem of the Arithmetic Mean. Purpose of the Chapter.

Catalog Record: Foundations of potential theory | Hathi Trust Digital Library

The Divergence Theorem for Normal Regions. Functions of One Variable; Regular Curves. Functions of Two Variables; Regular Surfaces. Functions of Three Variables.


Lightening of the Requirements with Respect to the Field. Stokes' Theorem for Regular Surfaces.

Development of Potentials in Series. Analytic Character of Newtonian Potentials. Development in Series of Spherical Harmonics.

Foundations Of Potential Theory

Development Valid at Great Distances. Behavior of Newtonian Potentials at Great Distances. Character of the Problem.


Lemmas on Improper Integrals. The Potentials of Volume Distributions.

Foundations of Potential Theory

The Potentials of Surface Distributions. The Potentials of Double Distributions. Preliminary Study of the Kernel kellogg potential theory Potential Theory The Integral Equation with Discontinuous Kernel The Characteristic Numbers of the Special Kernel Solution of the Boundary Value Problems Extensions; Further Propeties of U