Lq estimates for rearrangements of Fourier series

This work is concerned with estimating the upper envelopes S* of the absolute values of the partial sums of rearranged trigonometric sums. A.M. Garsia [Annals of Math. 79 (1964), 634-9] gave an estimate for the L₂ norms of the S*, averaged over all rearrangements of the original (finite) sum. This estimate enabled him to prove that the Fourier series of any function in L₂ can be rearranged so that it converges a.e. The main result of this thesis is a similar estimate of the L_q norms of the S*, for all even integers q. This holds for finite linear combinations of functions which satisfy a condition which is a generalization of orthonormality in the L₂ case. This estimate for finite sums is extended to Fourier series of L_q functions; it is shown that there are functions to which the Men’shov-Paley Theorem does not apply, but whose Fourier series can nevertheless be rearranged so that the S* of the rearranged series is in L_q.

Letters to the Honourable John H. Dunn, 1837-1838

The recipient of the letters is John Henry Dunn who was born on St. Helena (a British territory island of volcanic origin located in the South Atlantic Ocean) in 1792 to John Charles Dunn and Elizabeth Bazette. He was married to Charlotte Roberts on May 4th, 1820 and they had 6 sons and 2 daughters. He came to Canada in 1820 in which year he became the Receiver General for Canada. He held this position until 1841.Charlotte died in 1835. In 1822 he was named to the Province’s Legislative Council. He was president of the Welland Canal Company from 1825-1833. In 1836 he was named to the executive council of Upper Canada but resigned 3 weeks later with fellow counselors when lieutenant governor Sir Francis Bond refused the advice of the council. Dunn was made the Receiver General for the newly formed Province of Canada in 1841, and was elected to represent Toronto in the legislative assembly that year. He married his second wife on March 9th, 1842. Her name was Sophie-Louise Juchereau Duchsnay. They had a son and a daughter. In 1843 he resigned, and was not re-elected in 1844. He returned to England with his family and died in London on April 21, 1854. Dunn was a supporter of the Welland Canal, St. Lawrence Canals and other public improvements. Between the passage of the Canada Trade Act and the Act of the Union he had tried to insure that projects received funding despite financial constraints. He claimed that he has saved Upper Canada from bankruptcy. His son, Alexander Roberts Dunn received the Victoria Cross for his role in the Charge of the Light Brigade at Balaclava. Dunn Street in Niagara Falls is named after John Henry Dunn. The town and township of Dunnville were also named for him. Sources: http://biographi.ca/009004-119.01-e.php?id_nbr=3889 http://www.niagarafrontier.com/cityfalls.html

Dr. Stuart D. Scott Papers, 1837-2010 (non-inclusive)

Dr. Stuart D. Scott has written extensively in the fields of prehistory and history. As an archaeologist, he has traveled to some of the most significant sites in the world, including Pompeii, Stonehenge, the Valley of the Kings, Egypt’s pyramids and the Taj Mahal. He spent nine months excavating with the Tikal Project in Guatemala before returning to the University of Arizona where he received a Ph.D. in 1963. He excavated in New Zealand as a Fulbright scholar in 1963-1964. In the fall of 1964, Dr. Scott started a long career in the Anthropology Department of the State University of New York. He taught graduate and undergraduate archaeology courses and continued his archaeological and historical research. In 1979, Scott established the Old Fort Niagara Archaeology in Progress Project at Old Fort Niagara in Youngstown, New York. For many years, he became involved with historical archaeology in western New York. It was during this work that he became interested in the Upper Canada Rebellion of 1837-1838 and its aftermath. Dr. Scott and his wife, Patricia Kay Scott, would use Christmas breaks, summer vacations, and sabbatical years to travel. They were repeatedly lured back to the South Pacific, conducting research in New Zealand, Australia and many of the Micronesian and Polynesian islands. To tell the whole story of the Rebellion and the prison exiles, they traveled extensively in Canada, the United States, England and Tasmania to collect archival research and to experience the scenes of this remarkable narrative. In 2004, Dr. Scott published To the Outskirts of Habitable Creation: Americans and Canadians Transported to Tasmania in the 1840s, which told the story of the men captured, tried, convicted, and exiled as a result of the Rebellion, also called the Patriot War. Other contributions include: • A collaboration with Dr. Charles Cazeau on the book Exploring the Unknown, Great Mysteries Reexamined published by Plenum Press in 1979 • The Patriot Game: New Yorkers and the Canadian Rebellion of 1837-1838, which appeared in New York History, Vol. 68, No.3. 1987 • A Frontier Spirit: The Life of James Gemmell published in Australiasian Canadian Studies, Vol. 25, No. 2 2007 • To the Outskirts of Habitable Creation which appeared in the Friends of the National Archives, Vol. 20, No. 1 2009 • Numerous academic journal publications • Service on conference panels • Various research papers and proposals Before retiring in 1997 and while still a resident of Buffalo, N.Y., Dr. Scott spent considerable time with Brock University President Emeritus James A. Gibson and History Professor Colin Duquemin. The three shared a love of Rebellion history. It was largely because of this connection that Brock University was chosen as the recipient of Dr. Scott’s research materials.

Payment order for Samuel Adams on behalf of John Rice, 1772 July 1

Handwritten order to John Sale to pay scholarship funds to Samuel Adams for use by student John Rice (Harvard AB 1774), signed by Charles Chauncey, Thomas Waite, Jonathan Williams, and Daniel Marsh.

Letter from John T. Kirkland to Charles Sigourney,

This folder contains a typewritten copy of Kirkland's original letter. The location of the original is unknown.

Georges Bank, 1837 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Chart of Georges Shoal & Bank, surveyed by Charles Wilkes, Lieut. Commandant ... [et al.] in U.S. brig Porpoise, schooners Maria & Hadassah, by order of the Hon. Mahlon Dickerson, Secretary of the Navy ; drawn by J. Alden and W. May ; engraved by S. Stiles, Sherman & Smith, New-York. It was published under direction of the Navy Commissioners in 1837. Scale [ca. 1:62,000]. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'World Mercator' projection. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows hydrographic features such as as banks, shoals, bottom soil types, tide information, and more. Relief shown by soundings. Includes notes. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

Journal in America, 1837-1838,

"Number ... of ninety-nine copies printed." This copy not numbered.

Correspondence of Charlotte Grenville, Lady Williams Wynn, and her three sons, Sir Watkin Williams Wynn, bart., Rt. Hon. Charles Williams Wynn, and Sir Henry Williams Wynn...1795-1832.

Mode of access: Internet.

Duroc, duc de Frioul : grand maréchal du Palais impérial (1772-1813)

Mode of access: Internet.

The Greville memoirs (second part); a journal of the reign of Queen Victoria, from 1837 to 1852;

Preface signed: Henry Reeve.

The history of the party : from the rise of the whig and tory factions, in the reign of Charles II, to the passing of the reform bill.

Mode of access: Internet.