Partial Differential Equations

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Partial Differential Equations

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This course introduced the basic properties of separable Hilbert spaces, taking the space of sequences l^2 as the reference example. The properties of the Hilbert cube have been analyzed. The problem of the existence of a basis in an infinite dimensional vector (respectively Banach, and Hilbert) spa…

Giovanni Bellettini (Univ. of Roma Tor Vergata)

Aug 31, 2011 LATEST EPISODE
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59 EPISODES

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Latest episodes from Partial Differential Equations

11a Hahn-Banach theorems, III. (recorded 2011.03.16 at 14:00)

Play Episode Listen Later Aug 31, 2011 59:42

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11b Hahn-Banach theorems, III. (recorded 2011.03.16 at 15:00)

Play Episode Listen Later Aug 31, 2011 59:42

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12a Hahn-Banach theorems, IV. Banach-Steinhaus theorem. (recorded 2011.03.17 at 09:00)

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12b Hahn-Banach theorems, IV. Banach-Steinhaus theorem. (recorded 2011.03.17 at 10:00)

Play Episode Listen Later Aug 31, 2011 59:35

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13a The open mapping theorem. The closed graph theorem. (recorded 2011.03.18 at 09:00)

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13b The open mapping theorem. The closed graph theorem. (recorded 2011.03.18 at 10:00)

Play Episode Listen Later Aug 31, 2011 59:42

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14a The space of smooth functions with compact support: notion of convergence. Distributions. Criterion to be a distribution. Distributions representable by integration. (recorded 2011.03.23 at 14:00)

Play Episode Listen Later Aug 31, 2011 59:42

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14b The space of smooth functions with compact support: notion of convergence. Distributions. Criterion to be a distribution. Distributions representable by integration. (recorded 2011.03.23 at 15:00)

Play Episode Listen Later Aug 31, 2011 59:43

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15a Dirac delta. Principal value. Operations on distributions. (recorded 2011.03.24 at 09:00)

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15b Dirac delta. Principal value. Operations on distributions. (recorded 2011.03.24 at 10:00)

Play Episode Listen Later Aug 31, 2011 59:39

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16a Distributional derivative. Examples. Distributional laplacian of 1/|x| in R^3. (recorded 2011.03.25 at 09:00)

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16b Distributional derivative. Examples. Distributional laplacian of 1/|x| in R^3. (recorded 2011.03.25 at 10:00)

Play Episode Listen Later Aug 31, 2011 59:37

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17a Fundamental solution of a linear differential operator with constant coefficients. Examples: heat kernel. (recorded 2011.04.06 at 14:00)

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17b Fundamental solution of a linear differential operator with constant coefficients. Examples: heat kernel. (recorded 2011.04.06 at 15:00)

Play Episode Listen Later Aug 31, 2011 59:43

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18a Localization and support of a distribution. (recorded 2011.04.07 at 09:00)

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18b Localization and support of a distribution. (recorded 2011.04.07 at 10:00)

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19a On the support of a distribution. Convolution of distributions. Pull back of a distribution. (recorded 2011.04.08 at 09:00)

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19b On the support of a distribution. Convolution of distributions. Pull back of a distribution. (recorded 2011.04.08 at 10:00)

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20a The Fourier transform in L^1. Properties and examples. Fourier transform of e^{-|x|^2}. (recorded 2011.04.13 at 14:00)

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20b The Fourier transform in L^1. Properties and examples. Fourier transform of e^{-|x|^2}. (recorded 2011.04.13 at 15:00)

Play Episode Listen Later Aug 31, 2011 59:42

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21a Fourier transform and differentiation. On the inversion of the Fourier transform. (recorded 2011.04.14 at 09:00)

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21b Fourier transform and differentiation. On the inversion of the Fourier transform. (recorded 2011.04.14 at 10:00)

Play Episode Listen Later Aug 31, 2011 59:36

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22a Uncertainty principle. Rapidly decreasing functions: the Schwarz space. (recorded 2011.04.15 at 09:00)

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22b Uncertainty principle. Rapidly decreasing functions: the Schwarz space. (recorded 2011.04.15 at 10:00)

Play Episode Listen Later Aug 31, 2011 59:40

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23a Some properties of the Schwarz space. Fourier transform on the Schwarz space. Tempered distributions. (recorded 2011.04.20 at 14:00)

Play Episode Listen Later Aug 31, 2011 32:55

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23b Some properties of the Schwarz space. Fourier transform on the Schwarz space. Tempered distributions. (recorded 2011.04.20 at 15:00)

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24a The Fourier transform on tempered distributions. (recorded 2011.04.21 at 09:00)

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24b The Fourier transform on tempered distributions. (recorded 2011.04.21 at 10:00)

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25a Sobolev spaces with natural exponent. Characterization using the Fourier transform. Embedding in spaces C^k. (recorded 2011.04.27 at 14:00)

Play Episode Listen Later Aug 31, 2011 59:41

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25b Sobolev spaces with natural exponent. Characterization using the Fourier transform. Embedding in spaces C^k. (recorded 2011.04.27 at 15:00)

Play Episode Listen Later Aug 31, 2011 59:42

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26a Sobolev spaces with real exponent using the Fourier transform. Applications of the Fourier transform to linear elliptic PDEs. (recorded 2011.04.28 at 09:00)

Play Episode Listen Later Aug 31, 2011 59:40

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26b Sobolev spaces with real exponent using the Fourier transform. Applications of the Fourier transform to linear elliptic PDEs. (recorded 2011.04.28 at 10:00)

Play Episode Listen Later Aug 31, 2011 59:41

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27a Linear elliptic operators and Fourier transform. Poisson equation in the half-space. (recorded 2011.04.29 at 09:00)

Play Episode Listen Later Aug 31, 2011 59:41

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27b Linear elliptic operators and Fourier transform. Poisson equation in the half-space. (recorded 2011.04.29 at 10:00)

Play Episode Listen Later Aug 31, 2011 59:32

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28a Weak solutions of the non-homogeneous Poisson equation. Linear parabolic equations. The Cauchy problem and the Fourier transform. Qualitative properties of solutions. (recorded 2011.05.04 at 14:00)

Play Episode Listen Later Aug 31, 2011 59:42

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28b Weak solutions of the non-homogeneous Poisson equation. Linear parabolic equations. The Cauchy problem and the Fourier transform. Qualitative properties of solutions. (recorded 2011.05.04 at 15:00)

Play Episode Listen Later Aug 31, 2011 59:43

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29a Weak solutions of the non-homogeneous heat equation. The Cauchy problem for the wave equation. (recorded 2011.05.05 at 09:00)

Play Episode Listen Later Aug 31, 2011 59:42

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29b Weak solutions of the non-homogeneous heat equation. The Cauchy problem for the wave equation. (recorded 2011.05.05 at 10:00)

Play Episode Listen Later Aug 31, 2011 59:35

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30a Convolution and Fourier transform. Fundamental solutions. (recorded 2011.05.06 at 09:00)

Play Episode Listen Later Aug 31, 2011 59:42

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30b Convolution and Fourier transform. Fundamental solutions. (recorded 2011.05.06 at 10:00)

Play Episode Listen Later Aug 31, 2011 59:40

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01a Semi-inner and inner product space. (recorded 2011.02.09 at 14:00)

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01b Semi-inner and inner product space. (recorded 2011.02.09 at 15:00)

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02a Properties of l^2 space. (recorded 2011.02.10 at 09:00)

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02b Properties of l^2 space. (recorded 2011.02.10 at 10:00)

Play Episode Listen Later Aug 31, 2011 59:30

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03a Properties of l^2 space, Hilbert cube. (recorded 2011.02.11 at 09:00)

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03b Properties of l^2 space, Hilbert cube. (recorded 2011.02.11 at 10:00)

Play Episode Listen Later Aug 31, 2011 59:36

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04a Completion of a metric space. (recorded 2011.02.16 at 14:00)

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04b Completion of a metric space.(recorded 2011.02.16 at 15:00)

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05a Projection on a closed subspace of a Hilbert space. (recorded 2011.02.18 at 09:00)

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05b Projection on a closed subspace of a Hilbert space. (recorded 2011.02.18 at 10:00)

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06a Banach spaces. Linear operators on Banach spaces. (recorded 2011.02.23 at 14:00)

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