13.11 - 03.12 "The theory of Sobolev spaces", Professor G.V.Demidenko. MMF
From 13 November to 3 December 2011 at the Mechanics and Mathematics Faculty will be lectures held the head of the Laboratory of differential and difference equations Institute of Mathematics. S.L Sobolev SB RAS, Doctor of Physico-Mathematical Sciences, Professor G.V Demidenko. Lectures and consultations are conducted in accordance with the Program 020.of the Department of Fundamental Mathematics.
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ΠΠ°ΡΠ°
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ΠΠ°Π·Π²Π°Π½ΠΈΠ΅ ΡΠ΅ΠΌΡ
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ΠΠΈΠ΄ ΡΠ°Π±ΠΎΡΡ
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ΠΠ΅ΡΡΠΎ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ
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ΠΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΡΠ°ΡΠΎΠ²
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14.11.2011 ΠΏΠΎΠ½Π΅Π΄Π΅Π»ΡΠ½ΠΈΠΊ |
Chapter 1. Integral operators 1.1. Notation and basic theorems from mathematical analysis |
ΠΠ΅ΠΊΡΠΈΠΈ 15:05-15:55 16:10-17:00 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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15.11.2011 Π²ΡΠΎΡΠ½ΠΈΠΊ |
1.2. Space C ,L
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ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 11:25-12:15 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55 16:10-17:00 |
ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412 |
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16.11.2011 ΡΡΠ΅Π΄Π°
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1.3. Averaging operators, approximation by differentiable functions |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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17.11.2011 ΡΠ΅ΡΠ²Π΅ΡΠ³
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1.4. Fourier transform |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 11:25-12:15 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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18.11.2011 ΠΏΡΡΠ½ΠΈΡΠ°
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1.5. Laplace transform |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 11:25-12:15 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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19.11.2011 ΡΡΠ±Π±ΠΎΡΠ°
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1.6. Integral representations of functions |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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21.11.2011 ΠΏΠΎΠ½Π΅Π΄Π΅Π»ΡΠ½ΠΈΠΊ |
1.7. Integral representations of functions |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 11:25-12:15 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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22.11.2011 Π²ΡΠΎΡΠ½ΠΈΠΊ |
Chapter 1. Sobolev spaces 2.1. Weak derivatives |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 11:25-12:15 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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23.11.2011 ΡΡΠ΅Π΄Π°
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2.2. Basic theorems from mathematical analysis |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 11:25-12:15 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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24.11.2011 ΡΠ΅ΡΠ²Π΅ΡΠ³
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2.3. Approximation by differentiable functions |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 11:25-12:15 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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25.11.2011 ΠΏΡΡΠ½ΠΈΡΠ°
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2.4. Sobolev spaces C, L |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 11:25-12:15 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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26.11.2011 ΡΡΠ±Π±ΠΎΡΠ°
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2.5. Extension theorem |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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28.11.2011 ΠΏΠΎΠ½Π΅Π΄Π΅Π»ΡΠ½ΠΈΠΊ |
2.6. Fourier operators in spaces |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 11:25-12:15 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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29.11.2011 Π²ΡΠΎΡΠ½ΠΈΠΊ |
2.7. Laplace operators in spaces |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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30.11.2011 ΡΡΠ΅Π΄Π°
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2.8. Embedding theorems |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 11:25-12:15 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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01.12.2011 ΡΠ΅ΡΠ²Π΅ΡΠ³
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2.9. Trace theorems |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 11:25-12:15 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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02.12.2011 ΠΏΡΡΠ½ΠΈΡΠ°
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3. Pseudodifferential operators |
ΠΠ΅ΠΊΡΠΈΠΈ 10:20-11:10 11:25-12:15 ΠΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΠΈ 14:10-15:00 15:05-15:55
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ΠΠ΅Ρ Π°Π½ΠΈΠΊΠΎ-ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠ°ΠΊΡΠ»ΡΡΠ΅Ρ 412
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ΠΡΠΎΠ³ΠΈ |
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