Spatial dispersion, namely, the dependence of the dielectric-constant tensor on the wave vector (i.e., on the wavelength) at a fixed frequency, is receiving increased attention in electrodynamics and condensed-matter optics, partic ularly in crystal optics. In contrast to frequency dispersion, namely, the frequency dependence of the dielectric constant, spatial dispersion is of interest in optics mainly when it leads to qualitatively new phenomena. One such phenomenon has been weH known for many years; it is the natural optical activity (gyrotropy). But there are other interesting effects due to spatial dispersion, namely, new normal waves near absorption lines, optical anisotropy of cubic crystals, and many others. Crystal optics that takes spatial dispersion into account includes classical crystal optics with frequency dispersion only, as a special case. In our opinion, this fact alone justifies efforts to develop crystal optics with spatial dispersion taken into account, although admittedly its influence is smaH in some cases and it is observable only under rather special conditions. Furthermore, spatial dispersion in crystal optics deserves attention from another point as well, namely, the investigation of excitons that can be excited by light. We contend that crystal optics with spatial dispersion and the theory of excitons are fields that overlap to a great extent, and that it is sometimes quite impossible to separate them. It is our aim to show the true interplay be tween these interrelations and to combine the macroscopic and microscopic approaches to crystal optics with spatial dispersion and exciton theory."

In June 25-30, 1995 the NATO Advanced Research Workshop on" PhotoactifOrganic Materials: Science and Applications, devoted to organic materials and their specific responses to the light beam in view of their exploitation in devices was held in Novotel hotel in Avignon, France. It consisted ofplenary lectures, given by leading specialists in tbis field, shorter oral contributions and a poster session. Three working groups discussed more specific aspects related to (i) molecular engineering, (ii) electroluminescence and photorefractive effects as weil as (iii) nonlinear optical response of these materials, respectively. It allowed deeper insights into different problems and aspects of the workshop field. The conclusions of working groups were presented last day by their leaders. These pointed out the progress, problems encountered as weil as possible developments. The presentations have been followed by a plenary, brainstorm . discussion. The talks presented ranged around the working group subjects. Important progress was noted in the field of organic light emitted diodes (LEDls), as discussed and presented by several speakers. Light emission over the entire visible spectrum, from blue to red is possible with organic polymers. Tbis can be done on large, flexible surfaces with low cost. The best organic LEDls show actually the operation life time of 1600 to 1700 hours at room temperature. One expects their commercialization in the near future. Sirnilarly, important progress has been accomplished with photorefractive of merit for these materials are better than those for polymers.

Authored by well-known researchers, this book presents its material as accessible surveys, giving readers access to comprehensive coverage of results scattered throughout the literature. A unique source of information for graduate students and researchers in mathematics and theoretical physics, and engineers interested in the subject.

This EMS volume gives an overview of the modern theory of elliptic boundary value problems, with contributions focusing on differential elliptic boundary problems and their spectral properties, elliptic pseudodifferential operators, and general differential elliptic boundary value problems in domains with singularities.

Photonics concerns the generation, transport, processing and detection of light. It underlies a large amount of industrial activity, mainly devoted to information technology, telecommunications, environmental monitoring, biomedical science and instrumentation.

The field has received a powerful impetus recently with the introduction of nanoscale concepts. Moreover, organic materials now appear as key components in photonic devices such as light-emitting diodes, integrated lasers, or photovoltaic cells. Organic molecular systems offer unique opportunities in nanophotonics since both top-down and bottom-up strategies can be pursued towards the nanoscale.

This book gathers the proceedings of the NATO advanced research workshop on "Organic Nanophotonics," held in Aix-en-Provence, France, August 25-29, 2002. It constitutes a snapshot of the state of the art in the novel, emerging research area of nanophotonics based on organic molecules and materials.

Photonics concerns the generation, transport, processing and detection of light. It underlies a large amount of industrial activity, mainly devoted to information technology, telecommunications, environmental monitoring, biomedical science and instrumentation.

The field has received a powerful impetus recently with the introduction of nanoscale concepts. Moreover, organic materials now appear as key components in photonic devices such as light-emitting diodes, integrated lasers, or photovoltaic cells. Organic molecular systems offer unique opportunities in nanophotonics since both top-down and bottom-up strategies can be pursued towards the nanoscale.

This book gathers the proceedings of the NATO advanced research workshop on "Organic Nanophotonics," held in Aix-en-Provence, France, August 25-29, 2002. It constitutes a snapshot of the state of the art in the novel, emerging research area of nanophotonics based on organic molecules and materials.

A state of the art description of organic photo- and electroactive molecules and their practical applications. Topics covered include molecular design and synthesis of highly light sensitive molecules and phenomena associated with electron-photon interaction in organic molecules: nonlinear beam propagation, photorefractivity, multiphoton excitations and absorption, charge photogeneration and mobility, photo- and electroluminescence, photochromism and electrochromism, organic synthesis, material engineering and processing. Applications are addresses: optical data storage, LEDs, optical signalling processing, optical power limiters.

A state of the art description of organic photo- and electroactive molecules and their practical applications. Topics covered include molecular design and synthesis of highly light sensitive molecules and phenomena associated with electron-photon interaction in organic molecules: nonlinear beam propagation, photorefractivity, multiphoton excitations and absorption, charge photogeneration and mobility, photo- and electroluminescence, photochromism and electrochromism, organic synthesis, material engineering and processing. Applications are addresses: optical data storage, LEDs, optical signalling processing, optical power limiters.

This EMS volume gives an overview of the modern theory of elliptic boundary value problems, with contributions focusing on differential elliptic boundary problems and their spectral properties, elliptic pseudodifferential operators, and general differential elliptic boundary value problems in domains with singularities.

In June 25-30, 1995 the NATO Advanced Research Workshop on" PhotoactifOrganic Materials: Science and Applications, devoted to organic materials and their specific responses to the light beam in view of their exploitation in devices was held in Novotel hotel in Avignon, France. It consisted ofplenary lectures, given by leading specialists in tbis field, shorter oral contributions and a poster session. Three working groups discussed more specific aspects related to (i) molecular engineering, (ii) electroluminescence and photorefractive effects as weil as (iii) nonlinear optical response of these materials, respectively. It allowed deeper insights into different problems and aspects of the workshop field. The conclusions of working groups were presented last day by their leaders. These pointed out the progress, problems encountered as weil as possible developments. The presentations have been followed by a plenary, brainstorm . discussion. The talks presented ranged around the working group subjects. Important progress was noted in the field of organic light emitted diodes (LEDls), as discussed and presented by several speakers. Light emission over the entire visible spectrum, from blue to red is possible with organic polymers. Tbis can be done on large, flexible surfaces with low cost. The best organic LEDls show actually the operation life time of 1600 to 1700 hours at room temperature. One expects their commercialization in the near future. Sirnilarly, important progress has been accomplished with photorefractive of merit for these materials are better than those for polymers.

0. 1. The Scope of the Paper. This article is mainly devoted to the oper ators indicated in the title. More specifically, we consider elliptic differential and pseudodifferential operators with infinitely smooth symbols on infinitely smooth closed manifolds, i. e. compact manifolds without boundary. We also touch upon some variants of the theory of elliptic operators in Rn. A separate article (Agranovich 1993) will be devoted to elliptic boundary problems for elliptic partial differential equations and systems. We now list the main topics discussed in the article. First of all, we ex pound theorems on Fredholm property of elliptic operators, on smoothness of solutions of elliptic equations, and, in the case of ellipticity with a parame ter, on their unique solvability. A parametrix for an elliptic operator A (and A-). . J) is constructed by means of the calculus of pseudodifferential also for operators in Rn, which is first outlined in a simple case with uniform in x estimates of the symbols. As functional spaces we mainly use Sobolev - 2 spaces. We consider functions of elliptic operators and in more detail some simple functions and the properties of their kernels. This forms a foundation to discuss spectral properties of elliptic operators which we try to do in maxi mal generality, i. e., in general, without assuming selfadjointness. This requires presenting some notions and theorems of the theory of nonselfadjoint linear operators in abstract Hilbert space."

During the last decade our expertise in nanotechnology has advanced considerably. The possibility of incorporating in the same nanostructure different organic and inorganic materials has opened up a promising field of research, and has greatly increased the interest in the study of properties of excitations in organic materials. In this book not only the fundamentals of Frenkel exciton and polariton theory are described, but also the electronic excitations and electronic energy transfers in quantum wells, quantum wires and quantum dots, at surfaces, at interfaces, in thin films, in multilayers, and in microcavities. Among the new topics in the book are those devoted to the optics of hybrid Frenkel-Wannier-Mott excitons in nanostructures, polaritons in organic microcavities including hybrid organic-inorganic microcavities, new concepts for organic light emitting devices, the mixing of Frenkel and charge-transfer excitons in organic quasi one-dimensional crystals, excitons and polaritons in one and two-dimensional crystals, surface electronic excitations, optical biphonons, and Fermi resonances by polaritons. All new phenomena described in the book are illustrated by available experimental observations. The book will be useful for scientists working in the field of photophysics and photochemistry of organic solids (for example, organic light-emitting devices and solar cells), and for students who are entering this field. It is partly based on a book by the author written in 1968 - "Theory of Excitons" - in Russian. However the new book includes only 5 chapters from this version, all of which have been updated. The 10 new chapters contain discussions of new phenomena, their theory and their experimental observations.