{"title":"Alessandro Michelangeli","description":null,"products":[{"product_id":"inverse-linear-problems-on-hilbert-space-and-their-krylov-solvability-book-alessandro-michelangeli-9783030881580","title":"Inverse Linear Problems on Hilbert Space and their Krylov Solvability","description":"\u003cp\u003eThis book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector \u003ci\u003ef\u003c\/i\u003e in a Hilbert space \u003ci\u003eH\u003c\/i\u003e, a linear operator \u003ci\u003eA\u003c\/i\u003e acting on \u003ci\u003eH\u003c\/i\u003e, and a vector \u003ci\u003eg\u003c\/i\u003e in \u003ci\u003eH\u003c\/i\u003e satisfying \u003ci\u003eAf=g\u003c\/i\u003e, one is interested in approximating \u003ci\u003ef\u003c\/i\u003e by finite linear combinations of \u003ci\u003eg\u003c\/i\u003e, \u003ci\u003eAg\u003c\/i\u003e, \u003ci\u003eA\u003csup\u003e2\u003c\/sup\u003eg\u003c\/i\u003e, \u003ci\u003eA\u003csup\u003e3\u003c\/sup\u003eg\u003c\/i\u003e, … The closed subspace generated by the latter vectors is called the Krylov subspace of \u003ci\u003eH\u003c\/i\u003e generated by \u003ci\u003eg\u003c\/i\u003e and \u003ci\u003eA\u003c\/i\u003e. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text.\u003c\/p\u003e\u003cp\u003eAfter giving a broad introduction to the subject, examples and counterexamples of Krylov-solvable and non-solvable inverse problems are provided, together with results on uniqueness of solutions, classes of operators inducing Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations. An appendix collects material on weaker convergence phenomena in general projection methods.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis subject of this book lies at the boundary of functional analysis\/operator theory and numerical analysis\/approximation theory and will be of interest to graduate students and researchers in any of these fields.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52430909964561,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52430910685457,"sku":"NLS9783030881580","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783030881580.jpg?v=1785683643"},{"product_id":"advances-in-quantum-mechanics-book-alessandro-michelangeli-9783319589039","title":"Advances in Quantum Mechanics","description":"This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrödinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52482119532817,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52482120646929,"sku":"NLS9783319589039","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319589039.jpg?v=1786700635"},{"product_id":"advances-in-quantum-mechanics-book-alessandro-michelangeli-9783319865065","title":"Advances in Quantum Mechanics","description":"This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrödinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52500696826129,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":52500697547025,"sku":"NGR9783319865065","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319865065.jpg?v=1785918601"},{"product_id":"inverse-linear-problems-on-hilbert-space-and-their-krylov-solvability-book-no-caruso-9783030881610","title":"Inverse Linear Problems on Hilbert Space and their Krylov Solvability","description":"\u003cp\u003eThis book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector \u003ci\u003ef\u003c\/i\u003e in a Hilbert space \u003ci\u003eH\u003c\/i\u003e, a linear operator \u003ci\u003eA\u003c\/i\u003e acting on \u003ci\u003eH\u003c\/i\u003e, and a vector \u003ci\u003eg\u003c\/i\u003e in \u003ci\u003eH\u003c\/i\u003e satisfying \u003ci\u003eAf=g\u003c\/i\u003e, one is interested in approximating \u003ci\u003ef\u003c\/i\u003e by finite linear combinations of \u003ci\u003eg\u003c\/i\u003e, \u003ci\u003eAg\u003c\/i\u003e, \u003ci\u003eA\u003csup\u003e2\u003c\/sup\u003eg\u003c\/i\u003e, \u003ci\u003eA\u003csup\u003e3\u003c\/sup\u003eg\u003c\/i\u003e, … The closed subspace generated by the latter vectors is called the Krylov subspace of \u003ci\u003eH\u003c\/i\u003e generated by \u003ci\u003eg\u003c\/i\u003e and \u003ci\u003eA\u003c\/i\u003e. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text.\u003c\/p\u003e\u003cp\u003eAfter giving a broad introduction to the subject, examples and counterexamples of Krylov-solvable and non-solvable inverse problems are provided, together with results on uniqueness of solutions, classes of operators inducing Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations. An appendix collects material on weaker convergence phenomena in general projection methods.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis subject of this book lies at the boundary of functional analysis\/operator theory and numerical analysis\/approximation theory and will be of interest to graduate students and researchers in any of these fields.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52669601480977,"sku":"NLS9783030881610","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783030881610.jpg?v=1785810411"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-alessandro-michelangeli.oembed","provider":"World of Books ","version":"1.0","type":"link"}