Professor David Edmunds is Emeritus Professor of the Mathematics, Analysis and Partial Differential Equations Research Group at University of Sussex. His main research interests are functional analysis, interpolation theory, the theory of function spaces, sharp estimates of s-numbers and entropy numbers of embeddings and classical operators, and elliptic partial differential equations. He was awarded the LMS Polya prize in 1996, the Czech Academy of Sciences Bolzano prize in 1998, and was elected to a fellowship of the Learned Society of Wales in 2012.Professor Des Evans of Emeritus Professor of Mathematics at Cardiff University. His main research interests are in the spectral theory associated with differential equations and related areas of analysis and quantum mechanics. I was elected to a Fellowship of the Learned Society of Wales in 2010.

The abstract notions are beautifully presented... this is a complex, masterfully written research monograph suitable both for students as well as researchers.

• 1: Linear operators in Banach spaces 2: Entropy numbers, s-numbers, and eigenvalues 3: Unbounded linear operators 4: Sesqilinear forms in Hilbert spaces 5: Sobolve spaces 6: Generalized Dirichlet and Neumann boundary-value problems 7: Second-order differantial operators on arbitary open sets 8: Capacity and compactness criteria 9: Essential spectra 10: Essential spectra of general second-order differential operators 11: Global and asymptotic estimates for the eigenvalues 12: Estimates of the singular values Bibliography

Professor David Edmunds is Emeritus Professor of the Mathematics, Analysis and Partial Differential Equations Research Group at University of Sussex. His main research interests are functional analysis, interpolation theory, the theory of function spaces, sharp estimates of s-numbers and entropy numbers of embeddings and classical operators, and elliptic partial differential equations. He was awarded the LMS Polya prize in 1996, the Czech Academy of Sciences Bolzano prize in 1998, and was elected to a fellowship of the Learned Society of Wales in 2012.Professor Des Evans of Emeritus Professor of Mathematics at Cardiff University. His main research interests are in the spectral theory associated with differential equations and related areas of analysis and quantum mechanics. I was elected to a Fellowship of the Learned Society of Wales in 2010.

The abstract notions are beautifully presented... this is a complex, masterfully written research monograph suitable both for students as well as researchers.

• 1: Linear operators in Banach spaces 2: Entropy numbers, s-numbers, and eigenvalues 3: Unbounded linear operators 4: Sesqilinear forms in Hilbert spaces 5: Sobolve spaces 6: Generalized Dirichlet and Neumann boundary-value problems 7: Second-order differantial operators on arbitary open sets 8: Capacity and compactness criteria 9: Essential spectra 10: Essential spectra of general second-order differential operators 11: Global and asymptotic estimates for the eigenvalues 12: Estimates of the singular values Bibliography

Professor David Edmunds is Emeritus Professor of the Mathematics, Analysis and Partial Differential Equations Research Group at University of Sussex. His main research interests are functional analysis, interpolation theory, the theory of function spaces, sharp estimates of s-numbers and entropy numbers of embeddings and classical operators, and elliptic partial differential equations. He was awarded the LMS Polya prize in 1996, the Czech Academy of Sciences Bolzano prize in 1998, and was elected to a fellowship of the Learned Society of Wales in 2012.Professor Des Evans of Emeritus Professor of Mathematics at Cardiff University. His main research interests are in the spectral theory associated with differential equations and related areas of analysis and quantum mechanics. I was elected to a Fellowship of the Learned Society of Wales in 2010.

The abstract notions are beautifully presented... this is a complex, masterfully written research monograph suitable both for students as well as researchers.

• 1: Linear operators in Banach spaces 2: Entropy numbers, s-numbers, and eigenvalues 3: Unbounded linear operators 4: Sesqilinear forms in Hilbert spaces 5: Sobolve spaces 6: Generalized Dirichlet and Neumann boundary-value problems 7: Second-order differantial operators on arbitary open sets 8: Capacity and compactness criteria 9: Essential spectra 10: Essential spectra of general second-order differential operators 11: Global and asymptotic estimates for the eigenvalues 12: Estimates of the singular values Bibliography