Presents the classical theory of convergence of semigroups and looks at how it applies to real-world phenomena.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Adam Bobrowski is a professor and Chairman of the Department of Mathematics at Lublin University of Technology, Poland. He has authored over 50 scientific papers and two books, Functional Analysis for Probability and Stochastic Processes and An Operator Semigroup in Mathematical Genetics.
Inhaltsangabe
Preface 1. Semigroups of operators Part I. Regular Convergence: 2. The first convergence theorem 3. Example - boundary conditions 4. Example - a membrane 5. Example - sesquilinear forms 6. Uniform approximation of semigroups 7. Convergence of resolvents 8. (Regular) convergence of semigroups 9. Example - a queue 10. Example - elastic boundary 11. Example - membrane again 12. Example - telegraph 13. Example - Markov chains 14. A bird's-eye view 15. Hasegawa's condition 16. Blackwell's example 17. Wright's diffusion 18. Discrete-time approximation 19. Discrete-time approximation - examples 20. Back to Wright's diffusion 21. Kingman's n-coalescent 22. The Feynman-Kac formula 23. The two-dimensional Dirac equation 24. Approximating spaces 25. Boundedness, stablization Part II. Irregular Convergence: 26. First examples 27. Example - genetic drift 28. The nature of irregular convergence 29. Convergence under perturbations 30. Stein's model 31. Uniformly holomorphic semigroups 32. Asymptotic behavior of semigroups 33. Fast neurotransmitters 34. Fast neurotransmitters II 35. Diffusions on graphs and Markov chains 36. Semilinear equations 37. Coagulation-fragmentation equation 38. Homogenization theorem 39. Shadow systems 40. Kinases 41. Uniformly differentiable semigroups 42. Kurtz's theorem 43. A singularly perturbed Markov chain 44. A Tikhonov-type theorem 45. Fast motion and frequent jumps 46. Gene regulation and gene expression 47. Some non-biological models 48. Convex combinations of generators 49. Dorroh and Volkonskii theorems 50. Convex combinations in biology 51. Recombination 52. Recombination (continued) 53. Khasminskii's example 54. Comparing semigroups 55. Asymptotic analysis 56. Greiner's theorem 57. Fish dynamics 58. Emergence of transmission conditions 59. Emergence of transmission conditions II Part III. Convergence of Cosine Families: 60. Regular convergence 61. Cosines converge in a regular way Part IV. Appendices: 62. Laplace transform 63. Measurability implies continuity References Index.
Preface 1. Semigroups of operators Part I. Regular Convergence: 2. The first convergence theorem 3. Example - boundary conditions 4. Example - a membrane 5. Example - sesquilinear forms 6. Uniform approximation of semigroups 7. Convergence of resolvents 8. (Regular) convergence of semigroups 9. Example - a queue 10. Example - elastic boundary 11. Example - membrane again 12. Example - telegraph 13. Example - Markov chains 14. A bird's-eye view 15. Hasegawa's condition 16. Blackwell's example 17. Wright's diffusion 18. Discrete-time approximation 19. Discrete-time approximation - examples 20. Back to Wright's diffusion 21. Kingman's n-coalescent 22. The Feynman-Kac formula 23. The two-dimensional Dirac equation 24. Approximating spaces 25. Boundedness, stablization Part II. Irregular Convergence: 26. First examples 27. Example - genetic drift 28. The nature of irregular convergence 29. Convergence under perturbations 30. Stein's model 31. Uniformly holomorphic semigroups 32. Asymptotic behavior of semigroups 33. Fast neurotransmitters 34. Fast neurotransmitters II 35. Diffusions on graphs and Markov chains 36. Semilinear equations 37. Coagulation-fragmentation equation 38. Homogenization theorem 39. Shadow systems 40. Kinases 41. Uniformly differentiable semigroups 42. Kurtz's theorem 43. A singularly perturbed Markov chain 44. A Tikhonov-type theorem 45. Fast motion and frequent jumps 46. Gene regulation and gene expression 47. Some non-biological models 48. Convex combinations of generators 49. Dorroh and Volkonskii theorems 50. Convex combinations in biology 51. Recombination 52. Recombination (continued) 53. Khasminskii's example 54. Comparing semigroups 55. Asymptotic analysis 56. Greiner's theorem 57. Fish dynamics 58. Emergence of transmission conditions 59. Emergence of transmission conditions II Part III. Convergence of Cosine Families: 60. Regular convergence 61. Cosines converge in a regular way Part IV. Appendices: 62. Laplace transform 63. Measurability implies continuity References Index.
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