AIS - Harmonic Analysis and PDE

Speakers and Syllabus

 

 

NameoftheSpeaker with affiliation

 

No. of Lectures

 

DetailedSyllabus

Rahul Garg (IISER,Bhopal)

 

6

DistributionTheory

 

  1. Test function spaces and distributions, Calculus on distributions, Supports of distributions,Distributionasderivativesand tempered distribution, Fourier transform, Paley-Wiener theorem, Sobolev’s lemma, Sobolev Spaces.

  2. Applicationstodifferentialequations

(Fundamentalsolutions).

SundaramThangavelu (IISc Bangalore)

 

6

FourierAnalysisontheEuclideanspaces:

 

  1. Fourierseriesonthecircle.

  2. FouriertransformontheEuclideanspaces.

  3. Interpolation theorems: The Marcinkiewicz interpolation theorem (real method), the Riesz-Thorininterpolationtheorem(complex method), and interpolation of the analytic family of operators.

  4. Singularintegralsofconvolutiontype.

  5. Multipliertheorems:Marcinkiewiczmultiplier theorem, Mihlin–Hormander multiplier theorem.

 

 

 

 

  1. Singularintegralsofconvolutiontype.

  2. Multipliertheorems:Marcinkiewiczmultiplier theorem, Mihlin–Hormander multiplier theorem.

 

SanjayP.K. (NITCalicut)

 

6

HarmonicAnalysisontheHeisenbergGroup:

  1. ThegroupFouriertransformonthe Heisenberg group.

  2. Spectraltheoryofthesublaplacian.

  3. Bochner-Rieszmeansforthesublaplacian.

  4. AmultipliertheoremfortheFourier transform.

MousamiBhakta (IISER Pune)

 

6

EllipticPDEs

  1. WeakFormulationandellipticPDEs(Lax-Milgram theorem and its application, inhomogeneous boundary data problems).

  2. Well-posedness of elliptic PDEs with lower order perturbations (Fredholm alternatives).

  3. Boundary and Interior regularity of solutions of Elliptic PDEs.

  4. Unique Continuation Principles (UCP) of solution of Elliptic PDEs (if time permits).

Sombuddha Bhattacharyya

(IISERBhopal)

 

6

InverseProblems

  1. Calderón problem (Recovering a zeroth order perturbation of the Laplacian operator fromtheboundaryDirichlet-Neumannmap).

  2. An inverse problem for the Magnetic SchrödingerOperator(Assumingthe Carleman estimates).

  3. BoundaryandInteriorCarlemanestimates.

  4. Raytransformationoffunctions:Fourierslice theorem and explicit inversion of Ray transformation.

 

 

Time Table

 

 

 

 

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