08800nam 22007813 450 991097239270332120231110215903.097814704675241470467526(CKB)4940000000616274(MiAaPQ)EBC6798079(Au-PeEL)EBL6798079(RPAM)22488166(PPN)259970263(OCoLC)1275392867(EXLCZ)99494000000061627420211214d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierSpectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups1st ed.Providence :American Mathematical Society,2021.©2021.1 online resource (196 pages)Memoirs of the American Mathematical Society ;v.2729781470449360 1470449366 Includes bibliographical references.Cover -- Title page -- Acknowledgments -- Chapter 1. Introduction and main results -- 1.1. Characterization and properties of gL semigroups -- 1.2. Definition and properties of subsets of \Ne -- 1.3. Eigenvalue expansion and regularity of the gL semigroups -- 1.4. Convergence to equilibrium -- 1.5. Hilbert sequences and spectrum -- 1.6. Plan of the paper -- 1.7. Notation, conventions and general facts -- Chapter 2. Strategy of proofs and auxiliary results -- 2.1. Outline of our methodology -- 2.2. Proof of Theorem ??? (???) -- 2.3. Additional basic facts on gL semigroups -- Chapter 3. Examples -- Chapter 4. New developments in the theory of Bernstein functions -- 4.1. Review and basic properties of Bernstein functions -- 4.2. Products of Bernstein functions: new examples -- 4.3. Useful estimates of Bernstein functions on \C₊ -- Chapter 5. Fine properties of the density of the invariant measure -- 5.1. A connection with remarkable self-decomposable variables -- 5.2. Fine distributional properties of _{ } -- 5.3. Proof of Theorem ??? (???) -- 5.4. Small asymptotic behaviour of \nuh and of its successive derivatives -- 5.5. Proof of Theorem ??? -- 5.6. Proof of Theorem ??? -- 5.7. End of proof of Theorem ??? -- Chapter 6. Bernstein-Weierstrass products and Mellin transforms -- 6.1. Exponential functional of subordinators -- 6.2. The functional equations (???) and (???) on \R₊ -- 6.3. Proof of Theorem ??? -- 6.4. Proof of Proposition 6.1.2 -- 6.5. Proof of Theorem ??? (???): Bounds for ᵩ -- 6.6. Large asymptotic behaviours of ᵩ along imaginary lines -- 6.7. Proof of Theorem ??? (???) -- 6.8. Proof of Theorem 6.0.2 (2b): Examples of large asymptotic estimates of | ᵩ| -- Chapter 7. Intertwining relations and a set of eigenfunctions -- 7.1. Proof of Theorem ??? -- 7.2. End of the proof of the intertwining relation (7.3).7.3. Proofs of Theorem ??? (???) and (???) -- 7.4. Proof of the uniqueness of the invariant measure -- 7.5. Proof of Theorem ??? -- Chapter 8. Co-eigenfunctions: existence and characterization -- 8.1. Mellin convolution equations: distributional and classical solutions -- 8.2. Existence of co-eigenfunctions: Proof of Theorem ??? -- 8.3. The case ∈\Ne_{∞,∞}. -- 8.4. The case ∈\Ne_{∞}∖\Nii -- 8.5. The case ∈\Ne^{ }_{∞}. -- Chapter 9. Uniform and norms estimates of the co-eigenfunctions -- 9.1. Proof of Theorem 2.1.5 (1) via a classical saddle point method -- 9.2. Proof of Theorem 2.1.5 (2) via the asymptotic behaviour of zeros of the derivatives of -- 9.3. Proof of Theorem ??? (???) through Phragmén-Lindelöf principle -- Chapter 10. The concept of reference semigroups: \Lnu-norm estimates and completeness of the set of co-eigenfunctions -- 10.1. Estimates for the \lnu norm of \nun -- 10.2. Completeness of (\nun)_{ ≥0} in \lnu -- Chapter 11. Hilbert sequences, intertwining and spectrum -- 11.1. Proof of Theorem ??? -- Chapter 12. Proof of Theorems ???, ??? and ??? -- 12.1. Proof of Theorem 1.3.1 (2) -- 12.2. Proof of Theorem ??? (???) -- 12.3. Heat kernel expansion -- 12.4. Expansion of the adjoint semigroup: Proof of Theorem ??? -- 12.5. Proof of of Theorem ???: Rate of convergence to equilibrium -- Bibliography -- Back Cover."We provide the spectral expansion in a weighted Hilbert space of a substantial class of invariant non-self-adjoint and non-local Markov operators which appear in limit theorems for positive-valued Markov processes. We show that this class is in bijection with a subset of negative definite functions and we name it the class of generalized Laguerre semigroups. Our approach, which goes beyond the framework of perturbation theory, is based on an in-depth and original analysis of an intertwining relation that we establish between this class and a self-adjoint Markov semigroup, whose spectral expansion is expressed in terms of the classical Laguerre polynomials. As a by-product, we derive smoothness properties for the solution to the associated Cauchy problem as well as for the heat kernel. Our methodology also reveals a variety of possible decays, including the hypocoercivity type phenomena, for the speed of convergence to equilibrium for this class and enables us to provide an interpretation of these in terms of the rate of growth of the weighted Hilbert space norms of the spectral projections. Depending on the analytic properties of the aforementioned negative definite functions, we are led to implement several strategies, which require new developments in a variety of contexts, to derive precise upper bounds for these norms"--Provided by publisher.Memoirs of the American Mathematical Society Spectral theory (Mathematics)Nonselfadjoint operatorsLaguerre polynomialsPartial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theorymscOperator theory -- Groups and semigroups of linear operators, their generalizations and applications -- Markov semigroups and applications to diffusion processesmscApproximations and expansions -- Approximations and expansions -- Asymptotic approximations, asymptotic expansions (steepest descent, etc.)mscProbability theory and stochastic processes -- Distribution theory -- Infinitely divisible distributions; stable distributionsmscHarmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- General harmonic expansions, framesmscSequences, series, summability -- Inversion theorems -- Tauberian theorems, generalmscFunctions of a complex variable -- Entire and meromorphic functions, and related topics -- Functional equations in the complex domain, iteration and composition of analytic functionsmscIntegral transforms, operational calculus -- Integral transforms, operational calculus -- Transforms of special functionsmscSpectral theory (Mathematics)Nonselfadjoint operators.Laguerre polynomials.Partial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theory.Operator theory -- Groups and semigroups of linear operators, their generalizations and applications -- Markov semigroups and applications to diffusion processes.Approximations and expansions -- Approximations and expansions -- Asymptotic approximations, asymptotic expansions (steepest descent, etc.).Probability theory and stochastic processes -- Distribution theory -- Infinitely divisible distributions; stable distributions.Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- General harmonic expansions, frames.Sequences, series, summability -- Inversion theorems -- Tauberian theorems, general.Functions of a complex variable -- Entire and meromorphic functions, and related topics -- Functional equations in the complex domain, iteration and composition of analytic functions.Integral transforms, operational calculus -- Integral transforms, operational calculus -- Transforms of special functions.515/.722235P0547D0741A6060E0742C1540E0530D0544A20mscPatie Pierre1801548Savov Mladen1801549MiAaPQMiAaPQMiAaPQBOOK9910972392703321Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups4346895UNINA01088nam0 22002771i 450 UON0045909720231205105116.804978-96-459-6598-120151005d2015 |0itac50 baperIR|||| 1||||Zan-i ba zanbilmagmuʻe-ye dastanFarkhonde AqaʼiTehranNashr-e Neshane1394 [2015]150 p.22 cmLetteratura persianaNarrativaSec. 20-21UONC088118FIIRTihrānUONL005570IRA VI AEZIRAN - LETTERATURA - PERSIANO - TESTI LETTERARI - PERIODO MODERNO E CONTEMPORAAAQA'IFarkhondeUONV228458767094Našr-i NišānaUONV281830650ITSOL20250606RICASIBA - SISTEMA BIBLIOTECARIO DI ATENEOUONSIUON00459097SIBA - SISTEMA BIBLIOTECARIO DI ATENEOSI IRA VI AEZ 447 N SI 14794 7 447 N Zan-i ba zanbil1561538UNIOR03752nam 22006495 450 991037393500332120250609111345.01-4939-9934-610.1007/978-1-4939-9934-7(CKB)4100000009759141(DE-He213)978-1-4939-9934-7(MiAaPQ)EBC5971778(PPN)269147217(MiAaPQ)EBC5971509(EXLCZ)99410000000975914120191104d2019 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierParabolic Wave Equations with Applications /by Michael D. Collins, William L. Siegmann1st ed. 2019.New York, NY :Springer New York :Imprint: Springer,2019.1 online resource (IX, 135 p. 74 illus., 37 illus. in color.) 1-4939-9932-X This book introduces parabolic wave equations, their key methods of numerical solution, and applications in seismology and ocean acoustics. The parabolic equation method provides an appealing combination of accuracy and efficiency for many nonseparable wave propagation problems in geophysics. While the parabolic equation method was pioneered in the 1940s by Leontovich and Fock who applied it to radio wave propagation in the atmosphere, it thrived in the 1970s due to its usefulness in seismology and ocean acoustics. The book covers progress made following the parabolic equation’s ascendancy in geophysics. It begins with the necessary preliminaries on the elliptic wave equation and its analysis from which the parabolic wave equation is derived and introduced. Subsequently, the authors demonstrate the use of rational approximation techniques, the Padé solution in particular, to find numerical solutions to the energy-conserving parabolic equation, three-dimensional parabolic equations, and horizontal wave equations. The rest of the book demonstrates applications to seismology, ocean acoustics, and beyond, with coverage of elastic waves, sloping interfaces and boundaries, acousto-gravity waves, and waves in poro-elastic media. Overall, it will be of use to students and researchers in wave propagation, ocean acoustics, geophysical sciences and more.AcousticsNumerical analysisOceanographyDifferential equations, PartialGeophysicsAcousticshttps://scigraph.springernature.com/ontologies/product-market-codes/P21069Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Oceanographyhttps://scigraph.springernature.com/ontologies/product-market-codes/G25005Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Geophysics/Geodesyhttps://scigraph.springernature.com/ontologies/product-market-codes/G18009Acoustics.Numerical analysis.Oceanography.Differential equations, Partial.Geophysics.Acoustics.Numerical Analysis.Oceanography.Partial Differential Equations.Geophysics/Geodesy.534Collins Michael Dauthttp://id.loc.gov/vocabulary/relators/aut58770Siegmann William Lauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910373935003321Parabolic Wave Equations with Applications2527169UNINA05390nam 22007094a 450 991102000670332120200520144314.09786610740208978128074020612807402059780470073049047007304797804700730320470073039(CKB)1000000000355097(EBL)284362(OCoLC)437176195(SSID)ssj0000203339(PQKBManifestationID)11174117(PQKBTitleCode)TC0000203339(PQKBWorkID)10258874(PQKB)11441425(MiAaPQ)EBC284362(PPN)185060625(Perlego)2771486(EXLCZ)99100000000035509720060413d2007 uy 0engur|n|---|||||txtccrMining graph data /edited by Diane J. Cook, Lawrence B. HolderHoboken, N.J. Wiley-Intersciencec20071 online resource (501 p.)Description based upon print version of record.9780471731900 0471731900 Includes bibliographical references and index.MINING GRAPH DATA; CONTENTS; Preface; Acknowledgments; Contributors; 1 INTRODUCTION; 1.1 Terminology; 1.2 Graph Databases; 1.3 Book Overview; References; Part I GRAPHS; 2 GRAPH MATCHING-EXACT AND ERROR-TOLERANT METHODS AND THE AUTOMATIC LEARNING OF EDIT COSTS; 2.1 Introduction; 2.2 Definitions and Graph Matching Methods; 2.3 Learning Edit Costs; 2.4 Experimental Evaluation; 2.5 Discussion and Conclusions; References; 3 GRAPH VISUALIZATION AND DATA MINING; 3.1 Introduction; 3.2 Graph Drawing Techniques; 3.3 Examples of Visualization Systems; 3.4 Conclusions; References4 GRAPH PATTERNS AND THE R-MAT GENERATOR4.1 Introduction; 4.2 Background and Related Work; 4.3 NetMine and R-MAT; 4.4 Experiments; 4.5 Conclusions; References; Part II MINING TECHNIQUES; 5 DISCOVERY OF FREQUENT SUBSTRUCTURES; 5.1 Introduction; 5.2 Preliminary Concepts; 5.3 Apriori-based Approach; 5.4 Pattern Growth Approach; 5.5 Variant Substructure Patterns; 5.6 Experiments and Performance Study; 5.7 Conclusions; References; 6 FINDING TOPOLOGICAL FREQUENT PATTERNS FROM GRAPH DATASETS; 6.1 Introduction; 6.2 Background Definitions and Notation6.3 Frequent Pattern Discovery from Graph Datasets-Problem Definitions6.4 FSG for the Graph-Transaction Setting; 6.5 SIGRAM for the Single-Graph Setting; 6.6 GREW-Scalable Frequent Subgraph Discovery Algorithm; 6.7 Related Research; 6.8 Conclusions; References; 7 UNSUPERVISED AND SUPERVISED PATTERN LEARNING IN GRAPH DATA; 7.1 Introduction; 7.2 Mining Graph Data Using Subdue; 7.3 Comparison to Other Graph-Based Mining Algorithms; 7.4 Comparison to Frequent Substructure Mining Approaches; 7.5 Comparison to ILP Approaches; 7.6 Conclusions; References; 8 GRAPH GRAMMAR LEARNING; 8.1 Introduction8.2 Related Work8.3 Graph Grammar Learning; 8.4 Empirical Evaluation; 8.5 Conclusion; References; 9 CONSTRUCTING DECISION TREE BASED ON CHUNKINGLESS GRAPH-BASED INDUCTION; 9.1 Introduction; 9.2 Graph-Based Induction Revisited; 9.3 Problem Caused by Chunking in B-GBI; 9.4 Chunkingless Graph-Based Induction (Cl-GBI); 9.5 Decision Tree Chunkingless Graph-Based Induction (DT-ClGBI); 9.6 Conclusions; References; 10 SOME LINKS BETWEEN FORMAL CONCEPT ANALYSIS AND GRAPH MINING; 10.1 Presentation; 10.2 Basic Concepts and Notation; 10.3 Formal Concept Analysis10.4 Extension Lattice and Description Lattice Give Concept Lattice10.5 Graph Description and Galois Lattice; 10.6 Graph Mining and Formal Propositionalization; 10.7 Conclusion; References; 11 KERNEL METHODS FOR GRAPHS; 11.1 Introduction; 11.2 Graph Classification; 11.3 Vertex Classification; 11.4 Conclusions and Future Work; References; 12 KERNELS AS LINK ANALYSIS MEASURES; 12.1 Introduction; 12.2 Preliminaries; 12.3 Kernel-based Unified Framework for Importance and Relatedness; 12.4 Laplacian Kernels as a Relatedness Measure; 12.5 Practical Issues; 12.6 Related Work12.7 Evaluation with Bibliographic Citation DataThis text takes a focused and comprehensive look at mining data represented as a graph, with the latest findings and applications in both theory and practice provided. Even if you have minimal background in analyzing graph data, with this book you'll be able to represent data as graphs, extract patterns and concepts from the data, and apply the methodologies presented in the text to real datasets. There is a misprint with the link to the accompanying Web page for this book. For those readers who would like to experiment with the techniques found in this book or test their own ideas on graphData miningData structures (Computer science)Graphic methodsData mining.Data structures (Computer science)Graphic methods.005.74Cook Diane J.1963-1621465Holder Lawrence B.1964-1838904MiAaPQMiAaPQMiAaPQBOOK9911020006703321Mining graph data4417999UNINA