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Soardi P.M — Potential Theory On Infinite Networks
Soardi P.M — Potential Theory On Infinite Networks

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Название: Potential Theory On Infinite Networks

Автор: Soardi P.M

Аннотация:

The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds.
The book is intended for researchers with interdisciplinary interests in one of the following fields: Markov chains, combinatorial graph theory, network theory, Dirichlet spaces, potential theory, abstract harmonic analysis, theory of boundaries.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 204

Добавлена в каталог: 04.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
0-chain      9
0-chain, finite      9
1-chain      8
1-chain of finite energy      32
1-chain, finite      8
1-transitive      5 99
Associated Markov chain      14
Automorphism group      5 88 169
Automorphism group, compact      152 153
Automorphism group, topology      151
Automorphism of a graph      5
Automorphism of a network      7
Automorphism, bounded      73—76
Boundary      see "Royden’s boundary"
Boundary of $\overline{U}$      155
Boundary of a tile      126
Boundary of a tree      121—125
Boundary, combinatorial      82 155 170
Boundary, harmonic      134
Boundary, operator      9 115
Boundary, point (combinatorial)      20
Branch      see "Edge"
Branching continuous fraction      57
Canonical decomposition      54
Capacity      122
Cartesian product of graphs      77
Cascade, grounded      114
Cascade, ungrounded      109
Cascade, uniform      110 115 116
Cayley graph      16 120
Coboundary      10
Cochain      10
Conductance of an edge      7
Conductance of finite energy      33 39
Conductance, effective between a point and $\infty$      46
Conductance, effective between two points      25
Conductance, limit      38 39 73
Conductance, minimal      39 73
Conductance, sources (external)      12
Conductance, total      7 8 114 115
Conductance, uniqueness      18 35 72
Cutting edges      7
CYCLE      10
Cycle, finite      10 12 13
Cycle, spaces      38 115
Degree of a homogeneoue tree      6
Degree of a vertex      4
Degree, bounded      82 161
Dipole      9
Dirichlet, algebra      132 154
Dirichlet, finite function      34
Dirichlet, principle      29 51
Dirichlet, space      35
Dirichlet, sum      34
Distance (geodesic) in a graph      5 161
EDGE      3
Edge graph      126
Endpoints      3
ends      79 87 96
Ends of a tree      121
Energy of a 1-chain      28 32
Energy, sources      12
Exhaustion of a graph      4
Exhaustion of a network      8
Extension (of a 1-chain)      31
Extremal length      63
Extremities      see "Endpoints"
Flow      12
Flow of value m      100
Foster’s averaging formula      25 96
Fourier transform (on the torus)      105
Graph      3
Graph, connected      5
Graph, countable      5
Graph, locally finite      4
Graph, recurrent      17
Graph, transient      17
Graph, uniformly embedded      89
Green, function      17
Green, operator      17
Growth, exponential      82 125 127
Growth, linear      87
Growth, moderate      87 88 96 98 172
Growth, polynomial      75—77
Growth, subexponential      87 98
Harmonic function      19
Harmonic function, bounded and Dirichlet finite      62 131
Harmonic function, Dirichlet finite      59
Harmonic function, HD-minimal      139
Harmonic function, nonnegative      62
Harmonic, boundary      see "Boundary"
Harmonic, kernel      149
Harmonic, measure      146
Isomorphism of graphs      4
Isomorphism of networks      7
k-fuzz of a graph      162
Kirchhoff’s equations      12 13 33 34 115
Kirchhoff’s equations, homogeneous      14 72
Kirchhoff’s laws      see "Kirchhoff’s equations"
Laplacian (discrete)      16
Law of conservation of the energy      28 38 42
Length of a path      5
Limit set      93
Loop law      12
Lyons, better test of transience      51
Lyons, product of 1-chains      100
Lyons, simple criterion of transience      45
Minimum principle      20 135 136
Morphism of a graph      4
Morphism of a network      7
Nash — Williams theorem      55
Neighbour      4
Network, finite      22
Network, generalized      115
Network, recurrent      17
Network, transient      17
Node      see "Vertex"
Node law      12
Open-circuit resistance parameters      112
Orbit      87 169
Orientation of a graph      4
Path      5
Path, finite      5
Path, one-ended (one-sided)      5
Path, two-ended (two-sided)      5
Path, unbranched      119
Point      see "Boundary point" "Vertex"
Point, $G_{\delta}$      139
Point, interior      20
Point, isolated in $\Delta$      139 151
Poisson’s equation      16 34
Potential      13 24 43 49 108
Potential kernel      105 106
Random walk      17
Random walk, operator      16
Rayleigh’s principle      29 52
Resistance of an edge      7
Resistance, degree at a vertex      97
Resistance, effective between a node and $\infty$      45 51 54
Resistance, effective between two nodes      25 54
Resistance, limit      38 96
Resistance, minimal      42 96
Resistance, operator      12
Restriction of a 1-chain      39
Rough isometry      160
Roughly isometric      161
Royden’s boundary      134
Royden’s compactification      134
Royden’s decomposition theorem      60 132
Self-loop      4
Shorting vertices      8
Sobolev — Dirichlet inequality      86
Stage of a cascade      109 114
Strong isoperimetric inequality      82
Strong isoperimetric inequality and rough isometries      171
Strong isoperimetric inequality for hyperbolic graphs      95
Strong isoperimetric inequality for trees      119
Subgraph      4
Subgraph, induced      4
Subharmonic function      19
Subharmonic function, Dirichlet finite      46
Subnetwork      7
Subnetwork, compactification      154
Superharmonic function      19
Superharmonic function, Dirichlet finite      46
Superharmonic function, Evans      137
Superharmonic function, integral representation      146
Superharmonic function, nonnegative      20 61
Terminal of a cascade      110 114
Terminal of a tree      119
Thomson’s principle      28 41
Tile      125
Tiling      89 126
Transition probabilities      14 17
TREE      6
Tree, binary      153
Tree, homogeneous      6 19 57 119 145
Union of graphs      4
Uniqueness      32 72
Vertex      3
Vertex transitive      5
Virtanen’s theorem      62
Voltage generators (internal)      12
Walk      65
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