12 citations · 41 across the 34 of their papers we have counts for
4 papers · 1 filter
Laplace operators in finite energy and dissipation spaces
Sergey Bezuglyi, Palle E. T. Jorgensen
Recent applications of large network models to machine learning, and to neural network suggest a need for a systematic study of the general correspondence, (i) discrete vs (ii) con…
Markov operators generated by symmetric measures
Sergey Bezuglyi, Palle E. T. Jorgensen
With view to applications, we here give an explicit correspondence between the following two: (i) the set of symmetric and positive measures on one hand, and (ii) a certain fam…
Graph Laplace and Markov operators on a measure space
Sergey Bezuglyi, Palle E. T. Jorgensen
The main goal of this paper is to build a measurable analogue to the theory of weighted networks on infinite graphs. Our basic setting is an infinite -finite measure space $(V,…
Infinite-dimensional transfer operators, endomorphisms, and measurable partitions
Sergey Bezuglyi, Palle E. T. Jorgensen
We develop a new duality between endomorphisms of measure spaces, on the one hand, and a certain family of positive operators, called transfer operators, acting in spaces of measur…