Lectures on Brownian motion, heat conduction and potential theory: Spring 1965
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Danish |
| Published: |
Aarhus
Matematisk Inst.
1966
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| Series: | Matematisk Institut <Aarhus, Univ.>: Lecture notes series.
Nr. 3. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | getr.Pag. |
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Record in the Search Index
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| adam_text | CONTENTS
I SCHAUDER BASES
1.1 Haar orthonorma l system
1.2 Schauder basis of C 0,1^
1.3 Orthonormal set on 0,oo)
1 .h Schauder basis on 0,co)
1.5 Application
II THE BROWNIAN MOTION PROCESS AND WIENER MEASURES
2.1 Preliminaries
2.2 Construction of the process
2.3 Brownian motion process
2.h Markov property
2.5 Wiener measures
III THE STRONG MARKOV PROPERTY
3.2 The transition function and its associated semi group
of operators
3.2 An extension lemma and measurability
3.3 Extension of the Markov property
3 .*+ The Markov times
3.5 The strong Markov property
IV FIRST EXIT AND ENTRANCE TIMES
^.1 Choquet capacity
h.2 Preliminaries
^f.3 First entrance and exit times
h.h Hitting times and probabilities
*+.5 Regular points
V EXCESSIVE AND SUPERHARMONIC FUNCTIONS
REGULAR POINTS AND THIN SETS
5.1 More about Markov property
5.2 A sufficient condition for regularity and the Lebesgue
measure of the set of irregular points
5 3 Transition functions and transition densities
5.*+ Potential theoretic background
^.^ Excessive and superharmonic functions
5.6 Regularity and thinness
VI GREEN FUNCTIONS AND POTENTIALS
6.1 Fundamental solution of the heat equation
6.2 Principle of not feeling the boundary
6.3 Green functions for the Laplace operator and
Greenian domains
6.U Potentials
6.5 Newtonian capacity
VII DIRICHLET PROBLEM. BALAYAGE. ENERGY
7.1 Dirichlet problem
7.2 Dynkin s Lemma and its application
7.3 Balayage
7 M Energy
7.5 Energy and balayage
VIII SEMI CLASSICAL APPROACH TO POTENTIAL THEORY
8.1 Strong balayage
8.2 Strongly thin sets
8.3 Necessary condition for s thinness
Q.h S regular sets
8.5 Semi calssical sets
IX THE KAC CAPACITORY POTENTIALS
9.1 Analytic background
9.2 Measurability of sojourn times
9.3 Probability of spending a positive time in a given set
9.h The Kac capacitory potentials
9.5 Analytic formulas of Mark Kac
X BALAYAGE AND DIRICHLET PROBLEM IN THE KAC POTENTIAL
THEORY. APPLICATIONS
10.1 Probability interpretation of s thinness
10.2 First occupation time and strong balayage
10.3 Analytic results connected with strong balayage
and Dirichlet problem
10.h Balayage, energy and quasi s regular sets
10.5 Applications
|
| any_adam_object | 1 |
| author | Ciesielski, Zbigniew 1934-2020 |
| author_GND | (DE-588)108470032 |
| author_facet | Ciesielski, Zbigniew 1934-2020 |
| author_role | aut |
| author_sort | Ciesielski, Zbigniew 1934-2020 |
| author_variant | z c zc |
| building | Verbundindex |
| bvnumber | BV007170024 |
| classification_rvk | SI 430 SK 560 |
| ctrlnum | (OCoLC)468495705 (DE-599)BVBBV007170024 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV007170024 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:56:55Z |
| institution | BVB |
| language | Danish |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004580767 |
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| physical | getr.Pag. |
| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | Matematisk Inst. |
| record_format | marc |
| series | Matematisk Institut <Aarhus, Univ.>: Lecture notes series. |
| series2 | Matematisk Institut <Aarhus, Univ.>: Lecture notes series. |
| spelling | Ciesielski, Zbigniew 1934-2020 Verfasser (DE-588)108470032 aut Lectures on Brownian motion, heat conduction and potential theory Spring 1965 Aarhus Matematisk Inst. 1966 getr.Pag. txt rdacontent n rdamedia nc rdacarrier Matematisk Institut <Aarhus, Univ.>: Lecture notes series. Nr. 3. Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Wärmeleitung (DE-588)4064192-2 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Wärmeleitung (DE-588)4064192-2 s Brownsche Bewegung (DE-588)4128328-4 s Potenzialtheorie (DE-588)4046939-6 s Matematisk Institut <Aarhus, Univ.>: Lecture notes series. Nr. 3. (DE-604)BV002786062 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004580767&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ciesielski, Zbigniew 1934-2020 Lectures on Brownian motion, heat conduction and potential theory Spring 1965 Matematisk Institut <Aarhus, Univ.>: Lecture notes series. Potenzialtheorie (DE-588)4046939-6 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Wärmeleitung (DE-588)4064192-2 gnd |
| subject_GND | (DE-588)4046939-6 (DE-588)4079013-7 (DE-588)4128328-4 (DE-588)4064192-2 |
| title | Lectures on Brownian motion, heat conduction and potential theory Spring 1965 |
| title_auth | Lectures on Brownian motion, heat conduction and potential theory Spring 1965 |
| title_exact_search | Lectures on Brownian motion, heat conduction and potential theory Spring 1965 |
| title_full | Lectures on Brownian motion, heat conduction and potential theory Spring 1965 |
| title_fullStr | Lectures on Brownian motion, heat conduction and potential theory Spring 1965 |
| title_full_unstemmed | Lectures on Brownian motion, heat conduction and potential theory Spring 1965 |
| title_short | Lectures on Brownian motion, heat conduction and potential theory |
| title_sort | lectures on brownian motion heat conduction and potential theory spring 1965 |
| title_sub | Spring 1965 |
| topic | Potenzialtheorie (DE-588)4046939-6 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Wärmeleitung (DE-588)4064192-2 gnd |
| topic_facet | Potenzialtheorie Wahrscheinlichkeitstheorie Brownsche Bewegung Wärmeleitung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004580767&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002786062 |
| work_keys_str_mv | AT ciesielskizbigniew lecturesonbrownianmotionheatconductionandpotentialtheoryspring1965 |