Emerson, Whitman, and Hawthorne were all part of the New England Renaissance, the first great flourishing of literature in America. Emerson was arguably the most influential thinker of this period. He was part of the transcendentalist movement, which also included Margaret Fuller, editor of The Dial, and Emerson's friend and neighbor Henry David Thoreau. Emerson's essay "Self-Reliance" is a key document of transcendentalist thinking, which advocated for independence, free thinking, and a break with traditional religion. Emerson called for a national literature free from the influence of Europe and was greatly impressed with Whitman, to whom he wrote an encouraging letter.
Whitman took Emerson's ideas of independence and freedom to great heights in his poetry, notably his masterpiece, "Song of Myself." Like Emerson, Whitman was forging a new path and exploring both intellectual and artistic freedom in his work. Both Emerson and Whitman said "yes" to life and were not particularly interested in evil or the darker aspects of humanity, even though Whitman worked at a hospital during the Civil War. What they also share is that they are not systematic thinkers but take elements from various schools of thought and philosophy. Again, what they value is individual, personal freedom.
Hawthorne was an almost exact contemporary of Emerson and while they were part of the same intellectual and cultural environment, Hawthorne's imagination and view of life was considerably darker and more cynical. While he too saw the limitations of an inflexible religious ideology, he was nonetheless fascinated by it and explored it in The Scarlet Letter and multiple short stories. Emerson, by contrast, didn't seem all that interested in exploring ideas he disagreed with; he was a minster and famously broke with the church so that he could develop his thinking independently. Perhaps the most significant intellectual dialogue between Emerson and Hawthorne in terms of ideas and worldview can be found in Hawthorne's novel The Blithesdale Romance, a fictionalized account of Brook Farm, a utopian community.
For more on Emerson, pick up the biography The Mind on Fire. For more on Whitman, pick up Leaves of Grass.