His fields of research were broad, including algebra and mathematical analysis, in particular the very active field of functional analysis, and the still booming area of partial differential equations, especially boundary value problems. Apart from his seven books, there are some fifty research papers (that appeared in at least twenty-two different Journals or Conference Proceedings in fourteen countries), three memoirs (ranging from 23 to 101 pages), at least thirty-three seminar reports or mimeographed lecture notes (totalling 3,500 pages), plus six published Conference Proceedings (about 1,700 pages). ... His entire work reveals that he was a particular kind of analyst - one who derived his original experience from, and sought his goals in, the physical sciences. Even his most theoretical researches had a physical background or goal. This was perhaps one of the reasons for his great strength as a mathematician.

In recent years the use of such tools as operators in Hilbert and Banach spaces, the theory of distributions and other methods of functional analysis has become commonplace in investigations of problems in partial differential equations. Despite the very wide literature in this field there are but few books dealing with the subject from this point of view. The present book is designed to help fill this gap.

This book, taken together with Volume I, amounts to a rather complete 'cours d'analyse' in a modern vein. On the other hand, by a sound choice of topics and a wealth of good exercises, the classical tradition is not lost.

Garnir was an enthusiastically enterprising person. His dynamism, intelligently tempered by true kindness, permitted him to overcome the slowness and reticence sometimes encountered in university life. He communicated a great joy of life. It was a pleasure to sit at his table during a conference and to listen to him telling about his trips or episodes from university life; his kind cheerfulness was truly radiant. He was a man of exceptional pedagogical talents. His students were stimulated by his exemplary attitude, his scientific curiosity, the new paths of his research and the intensity of his work. He devoted his time and his experience to his students but also offered his friendship. He was attached to them and they to him. Essentially, Garnir was a man whose charisma, stability and true goodness were immensely beneficial to all who had the luck to have known him.

In 1964, Garnir consolidated his school at Liege by the establishment of a 'Centre of Functional Analysis of Liege' under his management and supervision .... At this Centre, at the time of his death, there were four professors, four 'chefs de travaux', three premier assistants and four assistants, as well as some five other collaborators. In early 1973, when the Centre was not even nine years old and adequate financial support was not forthcoming, opinions concerning the reputation of the Centre and its research achievements were requested from many mathematicians throughout the world. Already then some fifty mathematicians generally recognised that the Centre was Belgium's best known and most reputed centre of research in mathematics. Some of them noted that the only other comparable centre in Europe was the functional analysis group at the Polish Academy of Sciences at Warsaw. Others regarded the Centre as one of the best in the world in regard to functional analysis and its applications, because of its many expert members, both very young and older, of its team work on a large scale, and of its exceptionally many, highly qualified visitors who spent a few days or longer periods at the Centre. Thus from its very beginning it was a Centre of international cooperation in the broad realms of functional analysis and partial differential equations. Several hundred foreign mathematicians must have visited and/or lectured at Liege from 1960 onwards.