{"text_format":"2","workbook":"xls","n_sheets":1,"sheets":["report2"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":1,"defined_names":1,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"run_cost":"one","rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"report2","index":0,"n_rows":17,"n_cols":5,"rows_kept":17,"cut":false,"hidden":false,"merged":[[0,2,0,3],[0,4,0,5],[1,2,1,3],[1,4,1,5],[2,2,2,3],[2,4,2,5],[3,2,3,3],[5,2,5,3],[7,2,7,3],[8,2,8,3],[9,2,9,3],[10,2,10,3],[11,2,11,3],[12,2,12,3],[14,2,14,3]],"flags":["formulas_cached_only"]}
[null,"1.","Record Nr.",null,"UNINA9911046616003321"]
[null,null,"Autore",null,"Reinwand Simon"]
[null,null,"Titolo",null,"Functions of Bounded Variation : Theory  Methods  Applications"]
[null,null,"Pubbl/distr/stampa",null,"Göttingen : , : Cuvillier Verlag, , 2021"]
[{"$nulls":4},"©2021"]
[null,null,"ISBN",null,"9783736964037"]
[{"$nulls":4},"373696403X"]
[null,null,"Edizione",null,"[1st ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource (337 pages)"]
[null,null,"Disciplina",null,"515.6"]
[null,null,"Soggetti",null,"Functions of bounded variation"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Intro -- Preface -- Contents -- Introduction -- Chapter  1 Preliminaries -- 1.1 Classical Classes of Functions -- 1.2 Classes of Functions of Generalized Bounded  Variation -- Chapter 2  Functions with Primitive -- 2.1 The Kurzweil-Henstock Integral -- 2.2 Products of Derivatives -- 2.3 Compositions of Derivatives -- Chapter 3  Multiplier Spaces -- 3.1 Multipliers in Classical Spaces -- 3.2 Multipliers in Generalized BV-Spaces -- Chapter 4 Linear Operators between BV-Spaces -- 4.1 Multiplication Operators -- 4.2 Substitution Operators -- 4.3 Integral Operators -- Chapter 5 Nonlinear Operators between BV-Spaces -- 5.1 Composition Operators -- 5.2 Superposition Operators -- Chapter 6 Types of Convergence which Preserve Continuity -- 6.1 Five Types of Convergence in Comparison -- 6.2 Continuity of Composition Operators in BV -- Chapter 7 Integral Equations -- 7.1 Hammerstein Integral Equations -- 7.2 Volterra Integral Equations -- 7.3 Boundary and Initial Value Problems -- References."]
[null,null,null,"Sommario/riassunto","Funktionen beschränkter Variation sind in vielen Bereichen der Mathematik besonders wichtig. Diese Dissertation untersucht Räume von Funktionen einer Variable von beschränkter Variation unterschiedlichen Typs, vergleicht sie mit klassischen Funktionenräumen und enthüllt natürliche \"Lebensräume\" von BV-Funktionen. Neue und umfassende Ergebnisse über Abbildungseigenschaften wie Surjektivität und Injektivität, verschiedene Arten von Stetigkeit und Kompaktheit von linearen und nichtlinearen Operatoren zwischen solchen Räumen werden präsentiert. Eine neue Theorie über verschiedene Konvergenzarten von solchen Operatoren "]
[{"$nulls":4},"wird entwickelt und schließlich auf einen neuen Beweis für die Stetigkeit des Kompositionsoperators im klassischen BV-Raum angewendet. Diese abstrakten Ergebnisse dienen als Zutat für die Lösung von Hammerstein- und Volterra-Integralgleichungen mithilfe von Fixpunktsätzen. Diese liefern viele Kriterien, welche die Existenz und Eindeutigkeit von Lösungen garantieren, die sodann auf Anfangs- und Randwertprobleme in einem nichtklassischen Setting angewendet werden.Besonders Augenmerk liegt auf einer klaren und detaillierte Darstellung. Viele Abbildungen und Tabellen helfen, die wichtigsten Ideen zu visualisieren und zusammenzufassen. Über 160 Beispiele und Gegenbeispiele illustrieren die abstrakten Ergebnisse und zeigen deren Grenzen.Functions of bounded variation are most important in many fields of mathe¬matics. This thesis investigates spaces of functions of bounded variation with one variable of various types, compares them to other classical function spaces and reveals natural \"habitats\" of BV-functions. New and almost comprehensive results concerning mapping properties like surjectivity and injectivity, several kinds of continuity and compactness of both linear and nonlinear operators between such spaces are given. A new theory about different types of convergence of sequences of such operators is presented in full detail and applied to a new proof for the continuity of the composition operator in the classical BV-space. The abstract results serve as ingredients to solve Hammerstein and Volterra integral equations using fixed point theory. Many criteria guaranteeing the existence and uniqueness of solutions in BV-type spaces are given and later applied to solve boundary and initial value problems in a nonclassical setting. A big emphasis is put on a clear and detailed discussion. Many pictures and synoptic tables help to visualize and summarize the most important ideas. Over 160 examples and counterexamples illustrate the many abstract results and how delicate some of them are."]