Graph Laplace and Markov Operators on a Measure Space

Sergey Bezuglyi; Palle E. T Jorgensen

doi:10.1007/978-3-030-18484-1_3

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Book chapter

Graph Laplace and Markov Operators on a Measure Space

Sergey Bezuglyi and Palle E. T Jorgensen

Linear Systems, Signal Processing and Hypercomplex Analysis, pp.67-138

Operator Theory: Advances and Applications, Springer International Publishing

08/09/2019

DOI: 10.1007/978-3-030-18484-1_3

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Abstract

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 σ-finite measure space (V, B, μ) and a symmetric measure ρ on (V ×V,B×B) supported by a measurable symmetric subset E ⊂ V × V .

37B10

37L30

47L50

60J45

dissipation space

finite energy space

harmonic function

Laplace operator

Markov operator

Markov process

standard measure space

symmetric measure

Details

Title: Subtitle: Graph Laplace and Markov Operators on a Measure Space
Creators: Sergey Bezuglyi - University of Iowa
Palle E. T Jorgensen - University of Iowa
Resource Type: Book chapter
Publication Details: Linear Systems, Signal Processing and Hypercomplex Analysis, pp.67-138
Publisher: Springer International Publishing; Cham
Series: Operator Theory: Advances and Applications
DOI: 10.1007/978-3-030-18484-1_3
eISSN: 2296-4878
ISSN: 0255-0156
Language: English
Date published: 08/09/2019
Academic Unit: Mathematics
Record Identifier: 9984240773602771

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