Microlocal Day #2

Imperial College London, UK

3 December, 2010

 

Organisers

Claudia Garetto

Michael Ruzhansky

 

(Imperial College London)

 The workshop is related to the Daiwa Adrian Prize for the UK-Japan Collaboration

 

Conference Venue: Room 642 for 10am-1pm, and room 139 for 2pm-6:30pm, Huxley Building, Imperial College London

Address :     Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom

 

The Microlocal Day is a new initiative of a short and intensive series of lectures devoted to different aspects of the microlocal analysis and related topics. The program includes research lectures as well as survey lectures aimed at researchers and PhD students interested in the subject. All are welcome to attend.

The previous Microlocal Day #1 was held in June 2010.

Speakers

  • Fumihiko Hirosawa (Yamaguchi University, Japan)
  • Ilia Kamotski (University of Bath, UK)
  • Naoto Kumano-go (Kogakuin University, Japan)
  • Tokio Matsuyama (Tokai University, Japan)
  • Mitsuru Sugimoto (Nagoya University, Japan)
  • Mirko Tarulli (Imperial College London, UK)
  • Naohito Tomita (Osaka University, Japan)
  • Jens Wirth (University of Stuttgart, Germany)

 

Schedule

Friday, 3 December, 10:40am—1pm, Imperial College, Room 642

 

  • 10:40am Coffee/Tea
  • 11am Opening Ceremony
  • 11:05-11:45 Naohito Tomita (Osaka University, Japan) A Hörmander type multiplier theorem for multilinear operators
  • 11:55-12:25 Ilia Kamotski (University of Bath, UK) Boundary value problems in irregular domains and applications
  • 12:30-13:00 Mirko Tarulli (Imperial College London, UK) On the smoothing-Strichartz estimates

 

Friday, 3 December, 2pm—6:35pm, Imperial College, Room 139

 

  • 14:00-14:40 Fumihiko Hirosawa (Yamaguchi University, Japan) On the energy estimates for second order homogeneous hyperbolic equations with Levi-type conditions
  • 14:50-15:30 Jens Wirth (University of Stuttgart, Germany) Phase space analysis for hyperbolic systems
  • 15:40-16:20 Naoto Kumano-go (Kogakuin University, Japan) Path integrals for Gaussian processes as analysis on path space by time slicing approximation
  • 16:30-16:50 Coffee/Tea
  • 16:50-17:30 Tokio Matsuyama (Tokai University, Japan) Dispersion for 3D wave equation with a potential in an exterior domain
  • 17:40-18:20 Mitsuru Sugimoto (Nagoya University, Japan) On some Lp-type estimates for evolution operators
  • 18:30 Closing Ceremony

 

                                                                             

For further information please contact 
Michael Ruzhansky at this e-mail address 
 

Suggestion of hotels in the area (Earl’s Court Station, 15 mins walk to Imperial College)

 

Merlyn Court Hotel
Maranton House Hotel
Barkston Gardens
City Hotel Kensington
 
 

How to get to the Department of Mathematics, Imperial College London

 

Travel to the tube station Gloucester Road (District, Circle, and Piccadilly Lines).

When you exit the station, turn left along Gloucester Road, crossing Cromwell Road 50 meters from the exit.

After 4-5 minutes walk along Gloucester Road, turn right to Queen's Gate Terrace.

This is a short road leading directly to the entrance of the Huxley Building, at 180 Queen's Gate. We are on floor 6.

 

Abstracts

 

Fumihiko Hirosawa (Yamaguchi University) On the energy estimates for second order homogeneous hyperbolic equations with Levi-type conditions

 

We consider the energy estimates for the Cauchy problem of second order homogeneous

strictly hyperbolic equations with time dependent coefficients. In particular we focus

on the smoothness and interactions of oscillating coefficients, which are crucial for the

energy estimates; we shall call them a kind of Levi-type conditions.

 

Ilia Kamotski (University of Bath) Boundary value problems in irregular domains and applications

 

We discuss some aspects of the theory of the linear water waves, some challenges and

applications.

 

Naoto Kumano-go (Kogakuin University) Path integrals for Gaussian processes as analysis on path space by time slicing approximation

 

We introduce the path integrals for Gaussian processes as an analysis which has functional

integrals and smooth functional derivatives. More precisely, we give a fairly general class of

functionals so that the path integrals for Gaussian processes have a mathematically rigorous meaning.
For any functional belonging to our class, the time slicing approximation of the path integral

converges uniformly on compact subsets of the configuration space. Our class is closed under

addition, multiplication, translation, real linear transformation and functional differentiation.
The invariance under translation and orthogonal transformation, the interchange of the order

with Riemann-Stieltjes integrals and limits, the integration by parts and the Taylor expansion

formula with respect to functional differentiation, and the fundamental theorem of calculus

hold in the path integrals.
Reference:
[1] Naoto Kumano-go, Path integrals for Gaussian processes as analysis on path space by time slicing

approximation, Integration: Mathematical Theory and Applications, Vol. 1, No. 3 (2010), pp.253-278.

 

Tokio Matsuyama (Tokai University) Dispersion for 3D wave equation with a potential in an exterior domain

 

In this talk I will introduce the dispersive estimates and Strichartz estimates for 3D wave

equation with a potential in an exterior domain. The dispersive estimates will be proved by

interpolating between pointwise estimates for the propagator and $L^2$ estimates.

The pointwise estimates will be proved by using the spectral representation of the propagator.

The key lemma is the representation formula for the perturbed resolvent of the Schrödinger

operator in terms of the free resolvent in the whole space. By $TT^*$ argument we will

get the Strichartz estimates. 

 

Mitsuru Sugimoto (Nagoya University) On some Lp-type estimates for evolution operators

 

Mapping properties of unimodular Fourier multiplier describing various type of evolution operators

will be discussed. It is know that they are bounded on modulation spaces while not on Lp-spaces

except for the case p=2. In this talk, the boundedness between Lp-Sobolev spaces and modulation

spaces will be mainly considered. For the purpose, the inclusion relations between Lp-Sobolev

spaces and modulation spaces will be determined explicitly.

 

Mirko Tarulli (Imperial College London) On the smoothing-Strichartz estimates

 

We present some a-priori estimates for evolution equations in mixed smoothing-Strichartz spaces.

As an application we discuss Strichartz estimates for magnetic Klein-Gordon.

 

Naohito Tomita (Osaka University) A Hörmander type multiplier theorem for multilinear operators

 

In this talk, we consider a Hörmander type multiplier theorem for multilinear operators.

The multipliers in our problem have only the limited smoothness.

 

Jens Wirth (University of Stuttgart) Phase space analysis for hyperbolic systems

 

In this talk some aspects of phase space analysis for hyperbolic systems will be discussed.

The main focus will be on diagonalisation and decoupling of pseudo-differential hyperbolic

systems in adapted symbol classes taking care of the structure of the problem at infinity.

 

Program and all abstracts as a pdf file

 

Previously organised: Microlocal Day #1