The Theory of Distributions

图书简介

Many physical, chemical, biological and even economic phenomena can be modeled by differential or partial differential equations, and the framework of distribution theory is the most efficient way to study these equations. A solid familiarity with the language of distributions has become almost indispensable in order to treat these questions efficiently. This book presents the theory of distributions in as clear a sense as possible while providing the reader with a background containing the essential and most important results on distributions. Together with a thorough grounding, it also provides a series of exercises and detailed solutions. The Theory of Distributions is intended for master’s students in mathematics and for students preparing for the agregation certification in mathematics or those studying the physical sciences or engineering.

Preface ix Introduction xi Chapter 1 Topological Vector Spaces 1 1.1 Semi-norms 1 1.2 Topological vector space: definition and properties 2 1.3 Inductive limit topology 9 Chapter 2 Spaces of Test Functions 13 2.1 Multi-index notations 13 2.2 C function with compact support 14 2.3 Exercises with solutions 26 Chapter 3 Distributions on an Open Set of Rd 37 3.1 Definitions 37 3.2 Examples of distributions 39 3.3 Convergence of sequences of distributions 48 3.4 Exercises with solutions 55 Chapter 4 Operations on Distributions 75 4.1 Multiplication by a C function 75 4.2 Differentiation of a distribution 81 4.3 Transformations of distributions 100 4.4 Exercises with solutions 103 Chapter 5 Distribution Support 123 5.1 Distribution restriction and extension 123 5.2 Distribution support 126 5.3 Compact support distributions 132 5.4 Exercises with solutions 137 Chapter 6 Convolution of Distributions 151 6.1 Definition and examples 151 6.2 Properties of convolution 161 6.3 Exercises with solutions 167 Chapter 7 Schwartz Spaces and Tempered Distributions 179 7.1 S(Rd) Schwartz spaces 179 7.2 Tempered distributions 189 7.3 Exercises with solutions 196 Chapter 8 Fourier Transform 205 8.1 Fourier transform in L1(Rd) 205 8.2 Fourier transform in S(Rd) 220 8.2.1 Definition and first properties 220 8.3 Fourier transform in S(Rd) 230 8.4 Exercises with solutions 240 Chapter 9 Applications to ODEs and PDEs 263 9.1 Partial Fourier transform 263 9.2 Tempered solutions of differential equations 264 9.3 Fundamental solutions of certain PDEs 265 Appendix 269 References 275 Index 277

Trade Policy 买家须知

关于产品：
● 正版保障：本网站隶属于中国国际图书贸易集团公司，确保所有图书都是100%正版。
● 环保纸张：进口图书大多使用的都是环保轻型张，颜色偏黄，重量比较轻。
● 毛边版：即书翻页的地方，故意做成了参差不齐的样子，一般为精装版，更具收藏价值。
关于退换货：
由于预订产品的特殊性，采购订单正式发订后，买方不得无故取消全部或部分产品的订购。
由于进口图书的特殊性，发生以下情况的，请直接拒收货物，由快递返回：
● 外包装破损/发错货/少发货/图书外观破损/图书配件不全（例如：光盘等）
并请在工作日通过电话400-008-1110联系我们。
签收后，如发生以下情况，请在签收后的5个工作日内联系客服办理退换货：
● 缺页/错页/错印/脱线
关于发货时间：
一般情况下：
●【现货】下单后48小时内由北京（库房）发出快递。
●【预订】【预售】下单后国外发货，到货时间预计5-8周左右，店铺默认中通快递，如需顺丰快递邮费到付。
● 需要开具发票的客户，发货时间可能在上述基础上再延后1-2个工作日（紧急发票需求，请联系010-68433105/3213）；
● 如遇其他特殊原因，对发货时间有影响的，我们会第一时间在网站公告，敬请留意。
关于到货时间：
由于进口图书入境入库后，都是委托第三方快递发货，所以我们只能保证在规定时间内发出，但无法为您保证确切的到货时间。
● 主要城市一般2-4天
● 偏远地区一般4-7天
关于接听咨询电话的时间：
010-68433105/3213正常接听咨询电话的时间为：周一至周五上午8：30～下午5：00，周六、日及法定节假日休息，将无法接听来电，敬请谅解。
其它时间您也可以通过邮件联系我们：customer@readgo.cn,工作日会优先处理。
关于快递：
● 已付款订单：主要由中通、宅急送负责派送，订单进度查询请拨打010-68433105/3213。

The Theory of Distributions 分布理论：导论 数学史

The Theory of Distributions

分布理论：导论
数学史